Showing papers in "Physical Review D in 1982"

Quantum limits on noise in linear amplifiers

Abstract: How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.

Environment-induced superselection rules

Abstract: We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, "reduction of the wave packet," postulated by von Neumann to explain definiteness of an outcome of an individual observation, can be explained when a realistic model of an apparatus is adopted. Instead of an isolated quantum apparatus with a number of states equal to the number of possible distinct outcomes of the measurement, discussed by von Neumann, we consider an apparatus interacting with other physical systems, described here summarily as "environment." The interaction of the quantum apparatus with the environment results in correlations. Correlations impose effective superselection rules which prevent apparatus from appearing in a superposition of states corresponding to different eigenvalues of the privileged pointer observable. It is the propagation of the correlations with the pointer basis states which is ultimately responsible for the choice of the pointer observable. It can be thought of as a process of amplification in which the state of many distinct physical systems becomes correlated with the pointer basis state. Whether these environment systems are regarded as a part of the apparatus setup, or as a part of its environment is irrelevant. What is crucial is the redundancy of the record concerning the pointer observable which is imprinted into the correlations. Eigenspaces of the pointer observable provide a natural basis for the pointer of the quantum apparatus and determine the to-be-measured observable of the quantum system. Decay of those elements of the apparatus-system density matrix, which are off-diagonal in the pointer observable, is caused by the natural evolution of the combined system-apparatus-environment object. For a hypothetical finite environment with $N$ distinct eigenvalues of the apparatus-environment interaction Hamiltonian, off-diagonal terms will decay to become of the order of ${N}^{\ensuremath{-}\frac{1}{2}}$, and will recur only on a Poincar\'e time scale. No recurrences will be observed in realistic circumstances. As the correlations spread through the environment on a time scale typically much shorter than the recurrence time scale calculated for the environment already correlated with the pointer observable, the measurement becomes effectively irreversible. Relevance of this model of the measurement process for the understanding of the second law of thermodynamics and its relation to Bohr's "irreversible act of amplification" is briefly discussed. The emergence of the pointer observable can be interpreted as a clue about the resolution of the measurement problem in case of no environment. It points towards the possibility that properties of quantum systems have no absolute meaning. Rather, they must be always characterized with respect to other physical systems.

Neutrino decay and spontaneous violation of lepton number

Abstract: The orders of magnitude of decay rates for relatively light neutrinos are studied in the framework of the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) gauge group. The assumption is made that a hierarchy parameter $\ensuremath{\epsilon}(\ensuremath{\approx}(\mathrm{muon}\mathrm{mass})\textdiv{}[\mathrm{some}\mathrm{new}\mathrm{mass}\mathrm{scale}(\mathrm{possibly}\mathrm{much}\mathrm{smaller}\mathrm{than}\mathrm{the}\mathrm{grand}\mathrm{unification}\mathrm{scale})])$ plays a meaningful role in the full theory. For orientation it is first noted that the traditional $\ensuremath{ u}\ensuremath{\gamma}$ decay channel as well as the $3\ensuremath{ u}$ decay channel give neutrino lifetimes which for "typical" parameters are substantially longer than the age of the universe. Then we examine in detail some recent proposals which are claimed to result in greatly speeded-up decays into $\ensuremath{ u}$+Majoron, where the Majoron is a true Goldstone boson associated with spontaneous breakdown of lepton number. In a theory in which the usual Higgs doublet is augmented by a complex singlet (1-2 model) it is noted that the decay width into $\ensuremath{ u}$+Majoron actually vanishes to order ${\ensuremath{\epsilon}}^{5}$. In a theory where the doublet is augmented by a complex triplet (2-3 model) this decay is shown to vanish exactly, neglecting radiative corrections. A more general Majoron theory (1-2-3 model) is constructed and shown to also yield a vanishing tree-level decay rate for $\ensuremath{ u}$+Majoron decay to order ${\ensuremath{\epsilon}}^{5}$. Finally, the tree amplitudes in the 1-2 and 1-2-3 models are shown to give decay widths for $\ensuremath{ u}$+Majoron of order ${\ensuremath{\epsilon}}^{9}$ which correspond to lifetimes much greater than the age of the universe.

A Remnant of Chiral Symmetry on the Lattice

Abstract: A new criterion for chiral symmetry in lattice theories of fermions is derived within a block-spin formalism This "remnant" symmetry criterion properly incorporates the Adler Bell-Jackiw anomaly and avoids the fermion-doubling problem of other lattice fermion methods Some obstacles to implementing this approach in the presence of fully dynamical gauge fields are discussed

Neutrinoless double-β decay in SU(2)×U(1) theories

Abstract: It is shown that gauge theories give contributions to neutrinoless double-$\ensuremath{\beta}$ decay [${(\ensuremath{\beta}\ensuremath{\beta})}_{0\ensuremath{ u}}$] which are not covered by the standard parametrizations. While probably small, their existence raises the question of whether the observation of ${(\ensuremath{\beta}\ensuremath{\beta})}_{0\ensuremath{ u}}$ implies the existence of a Majorana mass term for the neutrino. For a "natural" gauge theory we argue that this is indeed the case.

Dynamical mass generation in continuum quantum chromodynamics

Abstract: We study the formation of a mass gap, or effective gluon mass (and consequent dimensionful parameters such as the string tension, glueball mass, $〈\mathrm{Tr}{{G}_{\ensuremath{\mu}\ensuremath{ u}}}^{2}〉$, correlation lengths) in continuum QCD, using a special set of Schwinger-Dyson equations. These equations are derived from a resummation of the Feynman graphs which represent certain gauge-invariant color-singlet Green's functions, and are themselves essentially gauge invariant. This resummation is essential to the multiplicative renormalizability of QCD in the light-cone gauge, which we adopt for technical reasons. We close the dynamical equations by "solving" a Ward identity, a procedure which, while exact in the infrared regime, is subject to ambiguities and corrections in the ultraviolet regime which are beyond the scope of the present work. (These ambiguities are less prominent for QCD in three dimensions, which we discuss also.) As discussed in an earlier work, quark confinement arises from a vortex condensate supported by the mass gap. Numerical calculations of the mass gap are presented, suggesting an effective gluon mass of 500\ifmmode\pm\else\textpm\fi{}200 MeV and a ${0}^{+}$ glueball mass of about twice this value.

Supersymmetry at ordinary energies. Masses and conservation laws

Abstract: An assessment is made of the general problems encountered in formulating a realistic supersymmetric theory in which the spontaneous breakdown of supersymmetry occurs at ordinary energies accessible to accelerators. As a starting point, three problems are identified in SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1) supersymmetric models with only quark and lepton chiral superfields: the up quarks get no masses, baryon and lepton ($B$ and $L$) conservation are violated by renormalizable and hence unsuppressed interactions, and the scalar counterparts of the quarks and leptons are too light. An interesting SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model of Dimopoulos and Georgi that avoids these problems is considered; it is found that this model contains $B$- and $L$-nonconserving effective interactions of dimensionality 5 that lead to proton decay at too rapid a rate. To guarantee natural $B$ and $L$ conservation in effective interactions of dimensionality 4 and 5, it is suggested that the gauge group that describes physics at ordinary energies contains a factor, such as another U(1), in addition to SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1). Such theories do not contain dimension-5 $L$-nonconserving interactions which could produce an observable neutrino mass, but they do allow dimension-6 $B$- and $L$-nonconserving interactions that would lead to proton decay at an observable rate. Supersymmetry is found to constrain the matrix elements for proton decay in a phenomenologically interesting way. A general explanation is given of how such theories naturally avoid the problem of light scalars, as found by Fayet. The formalism is used to derive general approximate mass relations for the scalar superpartners of the quarks and leptons. The problem of anomalies in the new U(1) current is considered, and one attractive scheme for avoiding them is offered, in which the anomalies cancel for precisely three generations of quarks and leptons.

Covariant Calculations at Finite Temperature: The Relativistic Plasma

Abstract: It is shown that finite-temperature calculations in field theory are manifestly Lorentz covariant at all stages if the Minkowski-space form of the temperature-dependent propagators is used and if the four-velocity ${u}_{\ensuremath{\mu}}$ of the heat bath is taken into account. New tensor structures involving ${u}_{\ensuremath{\mu}}$ generally arise but are severely constrained by covariant current conservation. A complete high-temperature ($T\ensuremath{\gg}m$) expansion of the vacuum polarization tensor for non-Abelian gauge theories is computed to order ${g}^{2}$ and displays the separate dependence on frequency $\ensuremath{\omega}$ and wave number $k$ that occurs at finite temperature. A covariant phenomenology of "electric" and "magnetic" properties is applied to the collective plasma effects, characterized by a plasma frequency ${{\ensuremath{\omega}}_{p}}^{2}=\frac{({N}_{f}+2N){g}^{2}{T}^{2}}{6}$ for $\mathrm{SU}(N)$ with ${N}_{f}$ fermions. The longitudinal normal modes of the "electric" field exist only for $\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$; for $\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$ all "electric" fields are screened. The transverse normal modes are plane waves along $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}\ifmmode\times\else\texttimes\fi{}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$ for $\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$; for $\ensuremath{\omega}l{\ensuremath{\omega}}_{p}$ both transverse "electric" and "magnetic" fields are shielded except for the static ($\ensuremath{\omega}=0$) case.

Bubble collisions in the very early universe

Abstract: It is believed that first-order phase transitions occurred in the very early universe when the temperature dropped below the grand-unification and Weinberg-Salam energies. Bubbles of the new, broken-symmetry phase would have formed surrounded by the symmetric phase. The energy released in the phase transition would have caused the walls of the bubbles to accelerate outwards. We study what happens when the walls collide with each other. We find that the energy in the walls would not be thermalized for a considerable time. In the inflationary-universe scenario, in which the bubble nucleation rate is low, thermalization could not occur until long after the baryon and nucleosynthesis eras and would not be complete. We also investigate the formation of primordial black holes in bubble collisions. The Weinberg-Salam phase transition is not likely to produce black holes but, under certain circumstances, the grand-unified phase transition might give rise to black holes of ${10}^{3}$ g.

Gravitational Effects upon Cosmological Phase Transitions

Abstract: The effects of spacetime curvature upon phase transitions in an expanding universe are investigated. We consider a Robertson-Walker model which is a radiation-dominated universe at early times and becomes de Sitter space at later times. In this universe the stability of a field theory containing a pair of interacting scalar fields is studied in first-order perturbation theory. It is noted that the crucial quantity in the stability analysis is $〈{\ensuremath{\varphi}}^{2}〉$, where $\ensuremath{\varphi}$ is a free scalar field. The behavior of $〈{\ensuremath{\varphi}}^{2}〉$ as a function of time is investigated, where both thermal and vacuum contributions are taken into account. It is shown that this behavior can be strongly affected by the coupling to the background gravitational field. Such coupling can cause $〈{\ensuremath{\varphi}}^{2}〉$ to decrease more slowly or even grow as the universe expands. This behavior can alter the evolution of the system and can result in either stabilization of an otherwise unstable field configuration or destabilization of an otherwise stable configuration.

Instability of flat space at finite temperature

Abstract: The instabilities of quantum gravity are investigated using the path-integral formulation of Einstein's theory. A brief review is given of the classical gravitational instabilities, as well as the stability of flat space. The Euclidean path-integral representation of the partition function is employed to discuss the instability of flat space at finite temperature. Semiclassical, or saddle-point, approximations are utilized. We show how the Jeans instability arises as a tachyon in the graviton propagator when small perturbations about hot flat space are considered. The effect due to the Schwarzschild instanton is studied. The small fluctuations about this instanton are analyzed and a negative mode is discovered. This produces, in the semiclassical approximation, an imaginary part of the free energy. This is interpreted as being due to the metastability of hot flat space to nucleate black holes. These then evolve by evaporation or by accretion of thermal gravitons, leading to the instability of hot flat space. The nucleation rate of black holes is calculated as a function of temperature.

Radiative decays of massive neutrinos

Abstract: General formulas are given for the decay rate ${\ensuremath{ u}}_{2}\ensuremath{\rightarrow}{\ensuremath{ u}}_{1}+\ensuremath{\gamma}$ in the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model for neutrinos with a small mass. The emphasis is on distinguishing between the cases of Dirac and Majorana neutrinos. Possible enhancements of the rate due to methods of eluding the Glashow-Iliopoulos-Maiani suppression and due to charged Higgs bosons are considered.

Fine-structure constant: Is it really a constant?

Abstract: It is often claimed that the fine-structure "constant" $\ensuremath{\alpha}$ is shown to be strictly constant in time by a variety of astronomical and geophysical results. These constrain its fractional rate of change $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}}}{\ensuremath{\alpha}}$ to at least some orders of magnitude below the Hubble rate ${H}_{0}$. We argue that the conclusion is not as straightforward as claimed since there are good physical reasons to expect $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}}}{\ensuremath{\alpha}}\ensuremath{\ll}{H}_{0}$. We propose to decide the issue by constructing a framework for $\ensuremath{\alpha}$ variability based on very general assumptions: covariance, gauge invariance, causality, and time-reversal invariance of electromagnetism, as well as the idea that the Planck-Wheeler length (${10}^{\ensuremath{-}33}$ cm) is the shortest scale allowable in any theory. The framework endows $\ensuremath{\alpha}$ with well-defined dynamics, and entails a modification of Maxwell electrodynamics. It proves very difficult to rule it out with purely electromagnetic experiments. In a cosmological setting, the framework predicts an $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}}}{\ensuremath{\alpha}}$ which can be compatible with the astronomical constraints; hence, these are too insensitive to rule out $\ensuremath{\alpha}$ variability. There is marginal conflict with the geophysical constraints; however, no firm decision is possible because of uncertainty about various cosmological parameters. By contrast the framework's predictions for spatial gradients of $\ensuremath{\alpha}$ are in fatal conflict with the results of the E\"otv\"os-Dicke-Braginsky experiments. Hence these tests of the equivalence principle rule out with confidence spacetime variability of $\ensuremath{\alpha}$ at any level.

Effective Fermion Masses of Order gT in High Temperature Gauge Theories with Exact Chiral Invariance

Abstract: It is shown that, at finite temperature, chiral invariance does not imply that fermion propagators have poles at ${K}^{2}=0$. Instead, a zero-momentum fermion has energy ${K}^{0}=M$, where ${M}^{2}=\frac{{g}^{2}C(R){T}^{2}}{8}$ and $C(R)$ is the quadratic Casimir of the fermion representation. The dispersion relation for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}\ensuremath{ e}0$ is computed and can be crudely approximated (to within 10%) by ${K}^{0}\ensuremath{\approx}{({M}^{2}+{\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}}^{2})}^{\frac{1}{2}}$. Applications to high-temperature QCD, SU(2)\ifmmode\times\else\texttimes\fi{}U(1), and grand unified theories are discussed.

Acceleration radiation and the generalized second law of thermodynamics

Abstract: It is shown that the Bekenstein limit, S/E< or =2..pi..R, for the entropy-to-energy ratio of matter confined by a box of size R is not needed for the validity of the generalized second law of thermodynamics. If one attempts to slowly lower a box containing rest energy E and entropy S into a black hole there will be an effective buoyancy force on the box caused by the acceleration radiation felt by the box when it is suspended near the black hole. As a result there is a finite lower bound on the energy delivered to the black hole in this process and thus a minimal area increase which turns out to be just sufficient to ensure that the generalized second law of thermodynamics is satisfied. By reversing this process, we can ''mine'' energy from a black hole. The nature of these processes is also analyzed from an inertial point of view and the mechanism by which energy is transported into and out of the black hole is explained. Analogous effects for accelerating boxes in flat spacetime are also analyzed.

Do narrow heavy multiquark states exist

Abstract: We discuss the existence of states made of four heavy quarks in the context of potential models already used in the study of heavy mesons and baryons. We first consider the situation where the quarks have the same mass and interact through a two-body potential due to color-octet exchange. In this case, we show that for any reasonable confining potential there is no state below the threshold corresponding to the spontaneous dissociation into two mesons. We investigate in detail different possibilities of modifying this negative result. This concerns the effect of hyperfine corrections, the case of orbitally excited states, the case of unequal quark masses, and the use of the static potential derived from the bag model treated in the adiabatic approximation.

Origin of the gravitational constant and particle masses in a scale-invariant scalar-tensor theory

Abstract: A viable scalar-tensor theory of gravitation is formulated by imposing global scale invariance to the matter part. Nonvanishing masses m of elementary particles as well as the gravitational constant G emerge through the cosmological background value of the scalar field. The scalar field maintains a dynamical degree of freedom in exchange for conformal invariance enjoyed otherwise by the gravity part. The temporal developments of G, m, and the scale factor of the Universe are determined simultaneously by solving coupled differential equations. In the simplest single-scalar model the result is not a variable-G theory in the usual sense. Departures from the standard theory occur through the time-dependent cosmological term. Of particular interest among the solutions are the asymptotically standard solutions.

Quantum mechanics of the gravitational field

Abstract: An approach to the quantum theory of gravitation is developed by analogy with the quantum mechanics of the simplest generally covariant system---the relativistic point particle. The central object in the formalism is the transition amplitude from one three-geometry to another which is given by a path integral. In that path integral one sums over all possible histories which connect two three-geometries separated by a given local proper time and then integrates over all possible proper-time separations. The choice of the range of integration for the proper time fixes the boundary conditions for the transition amplitude. If only positive proper times are allowed, the resulting amplitude is causal. A perturbation theory is developed in which the expansion parameter is the signature which takes the value minus one when the field histories (spacetimes) have hyperbolic signature and plus one for the Eclidean case. The "free" theory corresponds to zero signature and may be viewed as the result of replacing the Lorentz group as a symmetry group of the tangent spaces by one of its contractions, namely that one where the speed of light approaches zero. It is argued that besides the processes in which the universe starts or finishes at a singularity, there are also processes with a nonzero amplitude in which the universe starts and finishes in the same regular configuration without ever going through a singularity. These latter processes may be pictured as a loop in the configuration space of the gravitational field. The work remains formal throughout in that no definite meaning is given to the functional integrals considered.

Predictions of supersymmetric grand unified theories

Abstract: Renormalization effects are analyzed for a class of supersymmetric grand unified theories which contain the standard SU(3)/sub c/ x SU(2)/sub L/ x U(1) model. Predictions for sin/sup 2/theta-circumflex/sub W/(m/sub W/) and the proton lifetime are obtained as functions of ..lambda../sub M/S (MS is the modified minimal-subtraction scheme), N/sub H/ (number of relatively light Higgs doublets), and ..mu.. (the scale of supersymmetry breaking). For realistic input parameters we find 0.23 or approx. =tau/sub p/> or approx. =10/sup 29/ yr. Loop effects that could render the larger predicted values of sin/sup 2/theta-circumflex/sub W/(m/sub W/) consistent with experiment are described.

Measurement of neutrino-proton and antineutrino-proton elastic scattering

Abstract: We report here new measurements of neutrino-proton and antineutrino-proton elastic scattering, performed in the BNL neutrino beam. We observed a net signal of 212 neutrino events and 110 antineutrino events which lead to determination of the values ${R}_{\ensuremath{ u}}\ensuremath{\equiv}\frac{\ensuremath{\sigma}({\ensuremath{ u}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{ u}}_{\ensuremath{\mu}}+p)}{\ensuremath{\sigma}({\ensuremath{ u}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p)}=0.11\ifmmode\pm\else\textpm\fi{}0.015$, ${R}_{\overline{\ensuremath{ u}}}\ensuremath{\equiv}\frac{\ensuremath{\sigma}({\overline{\ensuremath{ u}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\overline{\ensuremath{ u}}}_{\ensuremath{\mu}}+p)}{\ensuremath{\sigma}({\overline{\ensuremath{ u}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+n)}=0.19\ifmmode\pm\else\textpm\fi{}0.035$, and ${R}^{\mathrm{NC}}\ensuremath{\equiv}\frac{\ensuremath{\sigma}({\overline{\ensuremath{ u}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\overline{\ensuremath{ u}}}_{\ensuremath{\mu}}+p)}{\ensuremath{\sigma}({\ensuremath{ u}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{ u}}_{\ensuremath{\mu}}+p)}=0.41\ifmmode\pm\else\textpm\fi{}0.09$ for $0.40l{Q}^{2}l0.90$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ where $\ensuremath{-}{Q}^{2}$ is the square of the momentum transfer to the nucleon. The differential cross sections as functions of ${Q}^{2}$, $\frac{d{\ensuremath{\sigma}}^{\ensuremath{ u}}}{d{Q}^{2}}$ and $\frac{d{\ensuremath{\sigma}}^{\overline{\ensuremath{ u}}}}{d{Q}^{2}}$, are also determined. Our results are in good agreement with the Weinberg-Salam-Glashow-Iliopoulos-Maiani model of the weak and electromagnetic interactions and yield ${{sin}^{2}\ensuremath{\theta}}_{W}=0.28\ifmmode\pm\else\textpm\fi{}0.03$.

Walls bounded by strings

Abstract: Extended structures consisting of walls bounded by strings appear in some unified gauge theories. The Spin(10) grand-unified-theory model provides the simplest example, provided the symmetry breaking proceeds via SU(4)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). It is shown that the presence of such structures may cause conflict with standard cosmology.

Thermal Stress Tensors in Static Einstein Spaces

Abstract: The Bekenstein-Parker Gaussian path-integral approximation is used to evaluate the thermal propagator for a conformally invariant scalar field in an ultrastatic metric If the ultrastatic metric is conformal to a static Einstein metric, the trace anomaly vanishes and the Gaussian approximation is especially good One then gets the ordinary flat-space expressions for the renormalized mean-square field and stress-energy tensor in the ultrastatic metric Explicit formulas for the changes in $〈{\ensuremath{\varphi}}^{2}〉$ and $〈{T}_{\ensuremath{\mu}\ensuremath{ u}}〉$ resulting from a conformal transformation of an arbitrary metric are found and used to take the Gaussian approximations for these quantities in the ultrastatic metric over to the Einstein metric The result for $〈{\ensuremath{\varphi}}^{2}〉$ is exact for de Sitter space and agrees closely with the numerical calculations of Fawcett and Whiting in the Schwarzschild metric The result for $〈{T}_{\ensuremath{\mu}\ensuremath{ u}}〉$ is exact in de Sitter space and the Nariai metric and is close to Candelas's values on the bifurcation two-sphere in the Schwarzschild metric Thus one gets a good closed-form approximation for the energy density and stresses of a conformal scalar field in the Hartle-Hawking state everywhere outside a static black hole

Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay

Abstract: After reviewing the current understanding of relativistic shock waves, a detailed analysis of relativistic detonation waves is presented. It is proposed that the motion of a detonation wave is analogous to the growth of a bubble nucleated during false vacuum decay at finite temperatures. Some possible applications of these results to cosmology are discussed.

Two-loop β function for a G 1 ×G 2 gauge theory

Abstract: The result is given for the two-loop $\ensuremath{\beta}$ function for a gauge group ${G}_{1}\ifmmode\times\else\texttimes\fi{}{G}_{2}$ including arbitrary representations of fermions and scalars. The extension to supersymmetric models is also given.

Classical and quantal Liouville field theory

Abstract: The canonical structure of the Liouville theory is investigated. We present two canonical transformations which map the theory onto a free field theory. The first makes use of conformal invariance and relies on a Yang-Feldman solution to the field equation. The second employs the inverse scattering method, which is uncommonly intricate, owing to the conformal invariance. We also analyze the quantized theory. Semiclassical arguments, supplemented by a study of the exact effective potential, suggest that the theory has a conformally invariant, continuous energy spectrum, bounded from below, but no translationally invariant ground state.

Hadronization by color bremsstrahlung

Abstract: Particle production in the central plateau of hadronic final states is calculated in a perturbative QCD model. We assume that the controlling process is bremsstrahlung of gluons. We find important differences between the spectrum produced in soft hadronic collisions and the spectrum in e+e annihilation. Describing soft hadronic collisions with the Low-Nussinov model, we find that the central plateau is independent of total energy, but depends strongly on the momentum transfer in the soft-gluon exchange. In contrast, the quark jets from e+e annihilation have a central plateau growing with energy. The strong momentum dependence in the hadron-induced plateau arises from the cancellations in the amplitude associated with the gauge invariance of the theory.

Finite-temperature symmetry breaking as Bose-Einstein condensation

Abstract: The effects of a net background charge on ideal and interacting relativistic Bose gases are investigated. For a non-Abelian symmetry only chemical potentials that correspond to mutually commuting charges may be introduced. The symmetry-breaking pattern is obtained by computing a $\ensuremath{\mu}$-dependent functional integral. We find that $\ensuremath{\mu}$ always raises the critical temperature and that below that temperature the existence of a ground-state expectation value for some scalar field produces Bose-Einstein condensation of a finite fraction of the net charge so as to keep the total charge fixed. (In the special, but familiar, case of total charge neutrality, the condensate contains equal numbers of particles and antiparticles.) There are four classes of results depending on whether volume or entropy is kept fixed and on whether the quadratic mass term ${m}^{2}$ is positive or negative.

Majorana Neutrinos and their Electromagnetic Properties

Abstract: To help develop a picture of Majorana neutrinos, we study their electromagnetic properties. We show that CPT invariance forbids a Majorana neutrino from having a magnetic or electric dipole moment. Then, by considering the process ..gamma --> nu..nu-bar, we find the most general expression for the matrix element of the electromagnetic current of a Majorana neutrino. The result is verified in a way which leads us to explore the behavior under parity of such a particle. Next, we see how electromagnetic properties which follow from one-loop diagrams conform to our general results. Finally, we show how the striking electromagnetic differences between Majorana and Dirac neutrinos can become invisible as the neutrino mass goes to zero.

Dyon-fermion dynamics

Abstract: We continue our study of the effect of light fermions on the charge degree of freedom of magnetic monopoles. Even though the gauge coupling is weak, the Fermi vacuum is strongly perturbed by its coupling to the charge degree of freedom of the monopole. To obtain a correct picture of the vacuum we concentrate on the lowest partial wave of the Fermi field about the monopole core. We find that this simplified system can be transformed to an equivalent one-dimensional scalar field theory in which the original fermions appear as sine-Gordon solitons and the monopole charge is determined by the expectation value of the scalar field at spatial infinity. The scalar theory, though not soluble, is sufficiently transparent for us to extract the qualitative physics of monopole charge in the presence of light fermions: the Witten formula for the dependence of monopole charge on vacuum angle, ${Q}_{n}=e(n\ensuremath{-}\frac{\ensuremath{\theta}}{2\ensuremath{\pi}})$, is true no matter how small the Fermi mass $m$; the fractional charge is spread through the Fermi vacuum over a region size ${m}^{\ensuremath{-}1}$ and the excitation energy of a charged state is of order $m$; the existence of vacuum structure on such a small energy scale means that certain exotic fermion-monopole scattering processes have very large cross sections. In particular it appears that in grand unification theories monopoles will catalyze baryon decay at typical strong-interaction rates.

Conserved charges from self-duality

Abstract: Given a simple self-dual quantum Hamiltonian $H=KB+\ensuremath{\Gamma}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$, where $K$ and $\ensuremath{\Gamma}$ are coupling constants, and the condition that $[B,[B,[B,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}]]]=16[B,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}]$, then we construct an infinite set of conserved charges ${Q}_{2n}$; $[H,{Q}_{2n}]=0$. In simple models, like the two-dimensional Ising or Baxter eight-vertex, these charges appear in the associated quantum theories and are equivalent to those which result from the transfer-matrix formulation and exact quantum integrability of the system. The power of our result is that it is an operator statement and does not refer to the number of dimensions or the nature of the space-time manifold: lattice, continuum, or loop space. It is suggested how the establishment of this link between duality and integrability could be used to exploit the Kramers-Wannier-type self-duality of the four-dimensional $\mathrm{SU}(N)$ gauge theory to find hidden symmetry.