Showing papers in "Physical Review D in 1973"

Black holes and entropy

Abstract: There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.

Radiative Corrections as the Origin of Spontaneous Symmetry Breaking

Abstract: We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. The scalar-to-vector mass ratio is computable as a power series in $e$, the electromagnetic coupling constant. We find, to lowest order, $\frac{{m}^{2}(S)}{{m}^{2}(V)}=(\frac{3}{2\ensuremath{\pi}})(\frac{{e}^{2}}{4\ensuremath{\pi}})$. We extend our analysis to non-Abelian gauge theories, and find qualitatively similar results. Our methods are also applicable to theories in which the tree approximation indicates the occurrence of spontaneous symmetry breakdown, but does not give complete information about its character. (This typically occurs when the scalar-meson part of the Lagrangian admits a greater symmetry group than the total Lagrangian.) We indicate how to use our methods in these cases.

Asymptotically Free Gauge Theories. I

Abstract: Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization-group techniques and their application to scaling phenomena. The renormalization-group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large spacelike momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3) \ifmmode\times\else\texttimes\fi{} SU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken and that the severe infrared singularities prevent the occurrence of noncolor singlet physical states. The deep-inelastic structure functions, as well as the electron-positron total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive light-cone or parton-model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

Generalized Hamiltonian dynamics

Abstract: Taking the Liouville theorem as a guiding principle, we propose a possible generalization of classical Hamiltonian dynamics to a three-dimensional phase space. The equation of motion involves two Hamiltonians and three canonical variables. The fact that the Euler equations for a rotator can be cast into this form suggests the potential usefulness of the formalism. In this article we study its general properties and the problem of quantization.

A Theory of Spontaneous T Violation

Abstract: A theory of spontaneous $T$ violation is presented. The total Lagrangian is assumed to be invariant under the time reversal $T$ and a gauge transformation (e.g., the hypercharge gauge), but the physical solutions are not. In addition to the spin-1 gauge field and the known matter fields, in its simplest form the theory consists of two complex spin-0 fields. Through the spontaneous symmetry-breaking mechanism of Goldstone and Higgs, the vacuum expectation values of these two spin-0 fields can be characterized by the shape of a triangle and their quantum fluctuations by its vibrational modes, just like a triangular molecule. $T$ violations can be produced among the known particles through virtual excitations of the vibrational modes of the triangle which has a built-in $T$-violating phase angle. Examples of both Abelian and non-Abelian gauge groups are discussed. For renormalizable theories, all spontaneously $T$-violating effects are finite. It is found that at low energy, below the threshold of producing these vibrational quanta, $T$ violation is always quite small.

Nonuniqueness of canonical field quantization in Riemannian space-time.

Abstract: We point out and discuss an ambiguity which arises in the quantum theory of fields when the background metric is not explicitly Minkowskian-in other words, when an external gravitational field, real or apparent, is present. A general theory of a canonical neutral scalar field in a static universe, including the construction of a Fock space, is presented. It is applied to a portion of two-dimensional flat space-time equipped with a non-Cartesian space-time coordinate system with respect to which the metric is nonetheless static. The resulting particle interpretation of the field is shown to be different from the standard one in special-relativistic free-field theory. The ambiguity frustrates an attempt to define uniquely the energy-momentum tensor by the usual method of normal ordering. We discuss various suggestions for (1) distinguishing a unique correct quantization in a given physical situation, or (2) reinterpreting seemingly inequivalent theories as physically equivalent. In passing it is shown that the vacuum state and the energy density of a free field in a box with periodic boundary conditions differ from those associated with a region of the same size in infinite space; this result should be of interest outside the gravitational context.

Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions

Abstract: An attempt is made to unify the fundamental hadrons and leptons into a common irreducible representation $F$ of the same symmetry group $G$ and to generate a gauge theory of strong, electromagnetic, and weak interactions. Based on certain constraints from the hadronic side, it is proposed that the group $G$ is SU(4\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(4\ensuremath{''}), which contains a Han-Nambu-type SU(3\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(3\ensuremath{''}) group for the hadronic symmetry, and that the representation $F$ is (4,4*). There exist four possible choices for the lepton number $L$ and accordingly four possible assignments of the hadrons and leptons within the (4,4*). Two of these require nine Han-Nambu-type quarks, three "charmed" quarks, and the observed quartet of leptons. The other two also require the nine Han-Nambu quarks, plus heavy leptons in addition to observed leptons and only one or no "charmed" quark. One of the above four assignments is found to be suitable to generate a gauge theory of the weak, electromagnetic, and SU(3\ensuremath{''}) gluonlike strong interactions from a selection of the gauges permitted by the model. The resulting gauge symmetry is $\mathrm{SU}{({2}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. The scheme of all three interactions is found to be free from Adler-Bell-Jackiw anomalies. The normal strong interactions arise effectively as a consequence of the strong gauges $\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. Masses for the gauge bosons and fermions are generated suitably by a set of 14 complex Higgs fields. The neutral neutrino and $\ensuremath{\Delta}S=0$ hadron currents have essentially the same strength in the present model as in other $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theories. The mixing of strong- and weak-gauge bosons (a necessary feature of the model) leads to parity-violating nonleptonic amplitudes, which may be observable depending upon the strength of SU(3\ensuremath{''}) symmetry breaking. The familiar hadron symmetries such as SU(3\ensuremath{'}) and chiral $\mathrm{SU}{({3}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}})}_{R}$ are broken only by quark mass terms and by the electromagnetic and weak interactions, not by the strong interactions. The difficulties associated with generating gauge interactions in the remaining three assignments are discussed in Appendix A. Certain remarks are made on the question of proton and quark stability in these three schemes.

Anharmonic Oscillator. II. A Study of Perturbation Theory in Large Order

Abstract: This paper is concerned with the nature of perturbation theory in very high order Specifically, we study the Rayleigh-Schrodinger expansion of the energy eigenvalues of the anharmonic oscillator We have developed two independent mathematical techniques (WKB analysis and difference-equation methods) for determining the large- n behavior of A K n , the n th Rayleigh-Schrodinger coefficient for the K th energy level We are not concerned here with placing bounds on the growth of A K n , as n , the order of perturbation theory, gets large Rather, we consider the more delicate problem of determining the precise asymptotic behavior of A K n , as n → ∞ for both the Wick-ordered and non-Wick—ordered oscillators Our results are in exact agreement with numerical fits obtained from computer studies of the anharmonic oscillator to order 150 in perturbation theory

Big-Bang Model Without Singularities

Abstract: A uniform cosmological model filled with fluid which possesses pressure and second viscosity is developed. The Einstein equations can be integrated exactly. One solution is the steady-state cosmology, but this is unstable. Other solutions start from the steady-state one in the infinite past but expand more and more slowly as viscosity dies out. At any finite proper time in the past the curvature is finite. Some comments on possible origins of this viscosity are given.

"Naive" Quark-Pair-Creation Model of Strong-Interaction Vertices

Abstract: We explicitly formulate the vacuum quark-pair-creation model (QPC) of strong-interaction vertices (Micu, Carlitz and Kislinger) in terms of the harmonic-oscillator spatial-SU(6) wave functions and an explicit vacuum quark-antiquark-pair transition matrix (both displaying the quark internal momenta). The coupling constants are expressed as functions of masses and the oscillator radius. The structure of the formulas is in agreement with the expressions coming from VMD (vector-meson dominance) and PCAC (partial conservation of axial-vector current), and the quark-model calculation of leptonic decays. We carefully investigate the relation of this QPC model with the additive quark model with elementary meson emission, which is known to explain most of the hadronic decays. We show that we recover this model in a given limit. It is shown that in this limit, a term $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{i})$ (depending on the internal quark momentum) appears in place of the usual $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}(i)\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\pi}}$ term; the additional contribution is similar to the well-known "recoil" term of Mitra and Ross. The main limits of the model lie (i) in the presence of a phenomenological pair-creation constant and (ii) in the nonrelativistic character of the treatment. A critical test of our model is provided by prediction of the decay-products polarization. We find a striking agreement with experiment for the crucial ${A}_{1}$ and $B$ decays. We make a comparison with the parameter-dependent model of Colglazier and Rosner.

Extraction of energy and charge from a black hole

Abstract: Misner has shown that in the scattering of massless wave fields by a Kerr black hole, certain modes are amplified at the expense of the rotational energy of the hole. We show here that the existence of this effect can be deduced from simple considerations based on Hawking's theorem that the area of a black hole can never decrease; no detailed examination of the wave equations is necessary. This new approach also reveals the existence of an analog of the Misner process in which a charged wave field is amplified upon being scattered by a charged black hole with consequent extraction of charge and Coulomb energy from the hole. Additional byproducts of this approach are a concise demonstration of the existence of a spin-spin force between a Kerr black hole and a nearby spinning particle, examples of the transcendence of the conservation laws for baryon and lepton numbers, and an example of a quantum violation of Hawking's theorem. The origin of this violation is discussed.

Quantum field-theory models in less than 4 dimensions

Abstract: The scalar ${\ensuremath{\lambda}}_{0}{\ensuremath{\varphi}}^{4}$ interaction and the Fermi interaction ${G}_{0}{(\overline{\ensuremath{\psi}}\ensuremath{\psi})}^{2}$ are studied for space-time dimension $d$ between 2 and 4. An unconventional coupling-constant renormalization is used: ${\ensuremath{\lambda}}_{0}={u}_{0}{\ensuremath{\Lambda}}^{\ensuremath{\epsilon}}$ ($\ensuremath{\epsilon}=4\ensuremath{-}d$) and ${G}_{0}={g}_{0}{\ensuremath{\Lambda}}^{2\ensuremath{-}d}$, with ${u}_{0}$ and ${g}_{0}$ held fixed as the cutoff $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$. The theories can be solved in two limits: (1) the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ where $\ensuremath{\varphi}$ and $\ensuremath{\psi}$ are fields with $N$ components, and (2) the limit of small $\ensuremath{\epsilon}$, as a power series in $\ensuremath{\epsilon}$. Both theories exhibit scale invariance with anomalous dimensions in the zero-mass limit. For small $\ensuremath{\epsilon}$, the fields $\ensuremath{\varphi}$, ${\ensuremath{\varphi}}^{2}$, and $\ensuremath{\varphi}{\ensuremath{ abla}}_{{\ensuremath{\alpha}}_{1}}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{ abla}}_{{\ensuremath{\alpha}}_{n}}\ensuremath{\varphi}$ all have anomalous dimensions, except for the stress-energy tensor. These anomalous dimensions are calculated through order ${\ensuremath{\epsilon}}^{2}$; they are remarkably close to canonical except for ${\ensuremath{\varphi}}^{2}$. The ${(\overline{\ensuremath{\psi}}\ensuremath{\psi})}^{2}$ interaction is studied only for large $N$; for small $\ensuremath{\epsilon}$ it generates a weakly interacting composite boson. Both the ${\ensuremath{\varphi}}^{4}$ and ${(\overline{\ensuremath{\psi}}\ensuremath{\psi})}^{2}$ theories as solved here reduce to trivial free-field theories for $\ensuremath{\epsilon}\ensuremath{\rightarrow}0$. This paper is motivated by previous work in classical statistical mechanics by Stanley (the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit) and by Fisher and Wilson (the $\ensuremath{\epsilon}$ expansion).

New Approach to the Renormalization Group

Abstract: A new set of renormalization-group equations is presented. These equations are based on a renormalization procedure in which counterterms are calculated for zero unrenormalized mass. Unlike the Gell-Mann-Low and Callan-Symanzik equations, they can be solved for arbitrary momenta. The solutions involve a momentum-dependent effective mass as well as a momentum-dependent effective coupling constant. By studying these solutions at large momenta, it can be shown that the nonleading terms discarded by previous authors do, in fact, remain negligible when the perturbation series is summed to all orders if, and only if, the effective mass vanishes at large momentum, which will be the case if a certain anomalous dimension is less than unity, as it is in asymptotically free theories. In this case, the new renormalization-group equations can be used at large momentum to derive not only the leading term, but the first three terms in an asymptotic expansion of any Green's function. These results are also applied to Wilson coefficient functions, and an important cancellation of anomalous dimensions is noted.

T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)

Abstract: The T-matrix formulation of electromagnetic scattering given previously by Waterman for the case of one scatterer is extended to the case of an arbitrary number of scatterers. The resulting total T matrix is expressed in terms of the individual T matrices by an iterative procedure. The essential tools used in the extension are the expansions associated with a translation of the origin for the spherical-wave solutions of Helmholtz's equation. The connection between these expansions and the unitary irreducible representations and associated local representations of the threedimensional Euclidean group E(3) is emphasized. Some applications to two spheres are given. (auth)

Pi pi Partial Wave Analysis from Reactions pi+ p ---> pi+ pi- Delta++ and pi+ p ---> K+ K- Delta++ at 7.1-GeV/c

Abstract: We present results of an energy-dependent phase-shift analysis for ππ energies between 550 and 1150 MeV from reactions π+p→π+π−Δ++ and π+p→K+K−Δ++ at 7.1 GeV/c. The I=0 s wave is parametrized in terms of a 2 × 2 M-matrix coupling ππ and KK¯ channels. All the obtained solutions rule out the possibility of a narrow e resonance in the ρ region and are characterized by a very rapid variation of the I=0 s-wave amplitude near KK¯ threshold. We show that this rapid variation can be explained by a pole in the second Riemann sheet close to the KK¯ threshold.

Radiating and nonradiating classical current distributions and the fields they generate

Abstract: Several general theorems are established relating to well-behaved, localized, monochromatic current distributions and the fields that they generate. In particular, a necessary and sufficient condition for such a current distribution to be nonradiating is established and a general expression for all nonradiating current distributions of this class is obtained.

Gravitational-wave observations as a tool for testing relativistic gravity

Abstract: Gravitational-wave observations can be powerful tools in the testing of relativistic theories of gravity---perhaps the only tools for distinguishing between certain extant theories in the foreseeable future. In this paper we examine gravitational radiation in the far field using a formalism that encompasses all "metric theories of gravity." There are six possible modes of polarization, which can be completely resolved by feasible experiments. We set forth a theoretical framework for classification of waves and theories, based on the Lorentz transformation properties of the six modes. We also show in detail how the six modes may be experimentally identified and to what extent such information limits the "correct" theory of gravity.

Perturbative Calculations of Symmetry Breaking

Abstract: The one-loop contributions to fermion and pseudo-Goldstone masses are calculated for the general class of renormalizable guage theories. It is shown explicitly that when the masses are subject to any type of zeroth-order symmetry. relation for all values of the parameters in the Lagrangian, the divergences in the one-loop corrections to these symmetry relations cancel. The finite parts of these corrections are evaluated and discussed. Other topics considered include the connection of this work with that of Coleman and E. Weinberg, the constraints obeyed by scalar coupling constants, and the path-integral derivation of the Feynman rules for general renormalizable gauge theories.

Dynamical Model of Spontaneously Broken Gauge Symmetries

Abstract: We demonstrate how a theory consisting of massless Fermi and vector-meson fields can lead to an excitation spectrum of solely massive particles. We eschew spinless Bose fields in the fundamental Lagrangian, contrary to current practice. A detailed model is presented and solved in lowest order. Fermion and axial-vector-meson masses are spontaneously generated, and the vector particle's mass is computed in terms of the fermion mass.

Quantized matter fields and the avoidance of singularities in general relativity

Abstract: We consider a classical gravitational field minimally coupled to a quantized neutral scalar field possessing mass. We are especially concerned with the effects of particle creation and quantum coherence on the premises and conclusions of the singularity theorems, which imply the inevitability of singularities in classical general relativity. A closed Robertson-Walker geometry is used throughout. Nongravitational interactions are not considered. The source of the gravitational field in the Einstein equations is the expectation value of the energy-momentum tensor of the quantized scalar field. Lacking a general prescription for obtaining a finite operator from the divergent formal expression for the energy-momentum tensor, we confine our attention to situations in which plausible special methods are available. We show that quantum coherence effects in this semiclassical model can result in a violation of the energy conditions which enter into the singularity theorems. Then we exhibit numerical solutions of the coupled Einstein and scalar field equations in which a Friedmann-like collapse is stopped and converted to a Friedmann-like expansion. (In this calculation one mode of the quantum field was assumed dominant.) We conclude that quantum effects of the type considered here can sometimes lead to avoidance of the cosmological singularity, at least on the time scale of one Friedmann expansion.

New Approach to Field Theory

Abstract: A field theory is quantized covariantly on Lorentz-invariant surfaces. Dilatations replace time translations as dynamical equations of motion. This leads to an operator formulation for Euclidean quantum field theory. A covariant thermodynamics is developed, with which the Hagedorn spectrum can be obtained, given further hypotheses. The Virasoro algebra of the dual resonance model is derived in a wide class of 2-dimensional Euclidean field theories.

Upper bounds on the values of masses in unified gauge theories

Abstract: Upper bounds are found for the masses of most of the new, unobserved particles in unified gauge theories by requiring that the partial-wave amplitudes satisfy unitarity bounds.

Coupled Anharmonic Oscillators. II. Unequal-Mass Case

Abstract: We develop a general formalism for calculating the large-order behavior of perturbation theory for quantized systems of unequal-mass coupled anharmonic oscillators. Our technique is based on a generalization of the semiclassical approximation which was used to study equal-mass oscillators in the first paper of this series. The unequal-mass problem is much more difficult because the path which minimizes the classical action is not a straight line. Assuming that this tunneling path is known, we derive a general expression for the physical-optics approximation to the wave function of a tunneling particle. This derivation rests on the construction of a WKB approximation in curved space. We thus completely reduce the general quantum problem to the much simpler classical one of determining the path. Then we present a perturbation scheme for finding the classical path for systems of oscillators whose masses only differ by a small amount. Finally, we illustrate our techniques by solving a two-mode unequal-mass oscillator and comparing these results with a computer calculation. Our theoretical predictions and numerical calculations agree.

Improved Treatment for the Infrared-Divergence Problem in Quantum Electrodynamics

Abstract: Although the conceptual difficulties associated with infrared divergences in quantum electrodynamics have long since been resolved, a convenient technique for identifying the appropriate infrared-finite part of Feynman graphs has been lacking. Such a technique is presented here. The polarization sums for both real and virtual photons are rearranged into two parts. One of these (called the $K$-polarization sum) resembles a gauge transformation whose structure permits a simple demonstration of infrared factorization and exponentiation. It is easy to see by inspection that the residual factors (with $G$-polarization sums) are infrared free. This is done for each separate graph, in contrast to earlier treatments where contributions from sets of graphs had to be considered together. The technique is illustrated by a detailed treatment of the radiative corrections to lowest-order potential scattering, and generalizations to other processes are indicated.

Scattering of Electromagnetic Radiation from a Black Hole

Abstract: The problem of propagation of electromagnetic waves in a gravitational field can be reduced to the problem of wave propagation in a material medium in flat space-time. This method is used here to calculate the scattering cross section of a Schwarzschild black hole and the polarization of the scattered wave. It is shown that the polarization of the wave (as measured at infinity) is not affected by the presence of the spherically symmetric gravitational field of the black hole. The light scattered from a rotating or "live" black hole is, however, expected to be polarized for an incident unpolarized plane wave. This may offer a new way to detect a live black hole.

Restricted Proof that the Weak Equivalence Principle Implies the Einstein Equivalence Principle

Abstract: Schiff has conjectured that the weak equivalence principle (WEP) implies the Einstein equivalence principle (EEP). A proof is presented of Schiff's conjecture, restricted to: (1) test bodies made of electromagnetically interacting point particles, that fall from rest in a static, spherically symmetric gravitational field; (2) theories of gravity within a certain broad class - a class that includes almost all complete relativistic theories that have been found in the literature, but with each theory truncated to contain only point particles plus electromagnetic and gravitational fields. The proof shows that every nonmentric theory in the class (every theory that violates EEP) must violate WEP. A formula is derived for the magnitude of the violation. It is shown that WEP is a powerful theoretical and experimental tool for constraining the manner in which gravity couples to electromagnetism in gravitation theories.

Quantum Tree Graphs and the Schwarzschild Solution

Abstract: It is verified explicitly to second order in Newton's constant, $G$, that the quantum-tree-graph contribution to the vacuum expectation value of the gravitational field produced by a spherically symmetric $c$-number source correctly reproduces the classical Schwarzschild solution. If the source is taken to be that of a point mass, then even the tree diagrams are divergent, and it is necessary to use a source of finite extension which, for convenience, is taken to be a perfect fluid sphere with uniform density. In this way both the interior and exterior solutions may be generated. A mass renormalization takes place; the total mass of the source, $m$, being related to its bare mass, ${m}_{0}$, and invariant radius, ${\ensuremath{\epsilon}}_{r}$, by the Newtonian-like formula, $m={m}_{0}\ensuremath{-}\frac{3Gm_{0}^{}{}_{}{}^{2}}{5{\ensuremath{\epsilon}}_{r}}+O({G}^{2})$, and the infinities in the quantum theory are seen to be a manifestation of the divergent self-energy problem encountered in classical mechanics.

Foundations for a Theory of Gravitation Theories

Abstract: A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (i) a glossary of fundamental concepts; (ii) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (iii) a conjecture (due to Schiff) that the weak equivalence principle implies the Einstein equivalence principle; and (iv) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

Surface Geometry of Charged Rotating Black Holes

Abstract: Invariant measures of the surface geometry of a charged rotating (Kerr-Newman) black hole are examined. It is shown that as the rotation rate of the black hole increases, the equatorial circumference increases while the polar circumference decreases. This is analogous to effects in material rotating bodies. The number of parameters describing a charged Kerr black hole drops from three to two on its surface. It is found that a scale parameter $\ensuremath{\eta}$ and a distortion parameter $\ensuremath{\beta}$ describe this geometry very simply. There emerge two classes of Kerr metrics separated by $\ensuremath{\beta}=\frac{1}{2}$. For larger $\ensuremath{\beta}$ the Gaussian curvature becomes negative on two polar-cap regions and the surface cannot be globally embedded in Euclidean 3-space. Possible physical effects are briefly discussed.

Tests for Neutral Currents in Neutrino Reactions

Abstract: Neutral currents predicted by weak-interaction models of the type discussed by Weinberg may be detected in neutrino reactions. Limits on the ratio $R$ of $\ensuremath{\sigma}(\ensuremath{ u}+N\ensuremath{\rightarrow}\ensuremath{ u}+X)$ to $\ensuremath{\sigma}(\ensuremath{ u}+N\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+X)$ are obtained independent of any dynamical assumption. For the total cross section for high-energy neutrinos, we find $R\ensuremath{\ge}0.18$, provided the Weinberg mixing angle satisfies ${{sin}^{2}\ensuremath{\theta}}_{W}\ensuremath{\le}0.33$. For the production of a single ${\ensuremath{\pi}}^{0}$ we find ${R}^{\ensuremath{'}}\ensuremath{\ge}0.50$ contrasted with the experimental result ${R}^{\ensuremath{'}}\ensuremath{\le}0.14$ using only the assumption of (3,3)-resonance dominance. Applications are also given to antineutrino reactions.