Showing papers on "Elementary particle published in 1969"

Quantized Fields and Particle Creation in Expanding Universes. I

Abstract: Spin-0 fields of arbitrary mass and massless fields of arbitrary spin are considered. The equations governing the fields are the covariant generalizations of the special-relativistic free-field equations. The metric, which is not quantized, is that of a universe with an expanding (or contracting) Euclidean 3-space. The spin-0 field of arbitrary mass is quantized in the expanding universe by the canonical procedure. The quantization is consistent with the time development dictated by the equation of motion only when the boson commutation relations are imposed. This consistency requirement provides a new proof of the connection between spin and statistics. We show that the particle number is an adiabatic invariant, but not a strict constant of the motion. We obtain an expression for the average particle density as a function of the time, and show that particle creation occurs in pairs. The canonical creation and annihilation operators corresponding to physical particles during the expansion are specified. Thus, we do not use an $S$-matrix approach. We show that in a universe with flat 3-space containing only massless particles in equilibrium, there will be precisely no creation of massless particles as a result of the expansion, provided the Einstein field equations without the cosmological term are correct. Furthermore, in a dust-filled universe with flat 3-space there will be precisely no creation of massive spin-0 particles in the limit of infinite mass, again provided that the Einstein field equations are correct. Conversely, without assuming any particular equations, such as the Einstein equations, as governing the expansion of the universe, we obtain the familiar Friedmann expansions for the radiation-filled and the dust-filled universes with flat 3-space. We only make a very general and natural hypothesis connecting the particle creation rate with the macroscopic expansion of the universe. In one derivation, we assume that in an expansion of the universe in which a particular type of particle is predominant, the type of expansion approached after a long time will be such as to minimize the average creation rate of that particle. In another derivation, we use the assumption that the reaction of the particle creation back on the gravitational field will modify the expansion in such a way as to reduce, if possible, the creation rate. This connection between the particle creation and the Einstein equations is surprising because the Einstein equations themselves played no part at all in the derivation of the equations governing the particle creation. Finally, on the basis of a so-called infinite-mass approximation, we argue that in the present predominantly dust-filled universe, only massless particles of zero spin might possibly be produced in significant amounts by the present expansion. In this connection, we show that massless particles of arbitrary nonzero spin, such as photons or gravitons, are not created by the expansion, regardless of its form.

Chiral SU ( 3 ) ⊗ SU ( 3 ) as a Symmetry of the Strong Interactions

Abstract: Starting with the modern developments of current algebra and the hypothesis of partially conserved axial-vector current, it has gradually become apparent that the strong interactions are almost invariant under the group $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$. In the limit that symmetry breaking is neglected, $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ does not appear as a symmetry of the particle states as $\mathrm{SU}(3)$ does, but rather as a symmetry realized by eight Goldstone bosons, i.e., the pseudoscalar octet. Most papers on $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ symmetry have been concerned with soft-meson theorems and their connection with effective Lagrangians. This paper is devoted to other aspects of the symmetry. Part of the paper is frankly pedagogical. The physics behind a symmetry realized by way of Goldstone bosons is brought out through a study of the $\ensuremath{\sigma}$ model. Then the general principles are stated abstractly and applied to the hadrons. One of the new results presented here is that there are two distinct ways in which $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ can be realized. In both cases there is an octet of massless pseudoscalar mesons. The two possibilities differ in the residual symmetry of the hadron spectrum: In one case, it is only $\mathrm{SU}(3)$; in the other, it is $\mathrm{SU}(3)$ times a discrete symmetry, which leads to parity doublets. It is conjectured that some of the observed parity doubling in nucleon resonances is a consequence of this new discrete symmetry. Symmetry breaking is discussed in detail and is found to be very complex. In particular, it is shown that, at least for the pseudoscalar-meson masses, octet enhancement can never occur for first-order perturbations around an $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$-symmetrical limit. Since octet enhancement is an empirical fact, one is forced to conclude that lowest-order perturbation theory is not a good approximation. In connection with octet enhancement, we show how one can use a principle of pole dominance in the angular momentum plane to replace scalar "tadpole" mesons with Regge trajectories.

Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher

Abstract: We analyze critically what happens when various interaction terms are added to a Lagrangian describing a free particle with spin \ensuremath{\ge}1. Good behavior results when the charged spin-one particle is coupled minimally to an external electromagnetic field or via a magnetic dipole moment. However, with an arbitrary electric quadrupole moment, the spin-one particle propagates noncausally ($vgc$) in an electrostatic field. Noncausal behavior is also found for the neutral vector field with self-coupling $\ensuremath{\lambda}{({W}_{\ensuremath{\mu}}{W}^{\ensuremath{\mu}})}^{2}$. Another kind of disease appears when the spin-two particle is given a charge: A constraint is converted into an equation of motion, so that there are six degrees of freedom instead of the desired five.

Interference effects in the radiative decay of closely spaced levels

Abstract: In this paper we present a study of the radiative decay of coherently excited, closely spaced, molecular (or atomic) levels. Interference effects in the decay process cannot be treated in general by displaying the damping matrix in a diagonal form, so that each decay channel is assumed to be characterized by its own lifetime. The problem of the radiative decay of coherently excited indistinguishable levels (characterized by the same symmetry) is treated by a self-consistent extension of the Wigner-Weisskopf method, or alternatively, by the ‘unitarity relations’ method, developed in elementary particles physics. Finally, the Fano configuration interaction method is applied for the decay of a manifold of states characterized by the same polarization. General expressions for photon counting rates are derived and the nature of a general quantum beat experiment is discussed.

Behavior of hadron collisions at extreme energies.

Abstract: There are several reasons to be interested in this problem of very high energy hadron scattering. Firstly, most theoretical inventions are based on analysis of simple collisions, in which only a small number of particles come out. But it is at once realized that questions of unitarity, the asymptotic behavior for high energy in dispersion integrals, etc, require some ansatz be made for the higher energy collisions, in order to close the infinite hierarchy of equations which result. Secondly, experiments at high energies usually yield many particles, and only by selecting the rare collision can we find those about which the theorist has been speaking. For the highly multiple inelastic collisions (to which the major part of the inelastic cross section is due) so many variables are involved that it is not known how to organize or present this data. Any theoretical suggestion (even if it proves to be not quite right) suggests a way that this vast amount of data may be analyzed. For this reason I shall present here some preliminary speculations on how these collisions might behave even though I have not yet analyzed them as fully as I would like.

High-Energy Collision Processes in Quantum Electrodynamics. I

Abstract: We have made a systematic study of all two-body elastic scattering amplitudes in quantum electro-dynamics at high energies. In particular, we have calculated the high-energy behavior of the following processes: (1) Delbr\"uck scattering, (2) electron Compton scattering, (3) photon-photon scattering, (4) electron-electron scattering, (5) electron-positron scattering, and (6) electron-proton scattering. The processes (1) and (2) are calculated up to the sixth order in the coupling constant $e$, the process (3) up to the eighth order, and the processes (4), (5), and (6) up to the fourth order. Our calculations show that all of these amplitudes are proportional to $s$, the square of the center-of-mass energy, as $s$ becomes large. In other words, we have found that, to these orders, ${\mathrm{lim}}_{s\ensuremath{\rightarrow}\ensuremath{\infty}}\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ exists and is nonzero for all $t\ensuremath{ e}0$, where $\ensuremath{-}t$ is the square of the momentum transfer. Furthermore, we found it meaningful to assign a factor (we call it the impact factor) to each particle. More precisely, for the high-energy scattering of $a+b\ensuremath{\rightarrow}a+b$, the imaginary coefficient of $s$ for the scattering amplitude is proportional to $\ensuremath{\int}d{\mathbf{q}}_{\ensuremath{\perp}}{[{({\mathbf{q}}_{\ensuremath{\perp}}+{\mathbf{r}}_{1})}^{2}]}^{\ensuremath{-}1}{[{({\mathbf{q}}_{\ensuremath{\perp}}\ensuremath{-}{\mathbf{r}}_{1})}^{2}]}^{\ensuremath{-}1}{\mathcal{I}}^{a}({\mathbf{r}}_{1},{\mathbf{q}}_{1}){\mathcal{I}}^{b}({\mathbf{r}}_{1},{\mathbf{q}}_{\ensuremath{\perp}})$, where 2r1 is the momentum transfer, and ${\mathcal{I}}^{a}({\mathbf{r}}_{1},{\mathbf{q}}_{\ensuremath{\perp}})$ and ${\mathcal{I}}^{b}({\mathbf{r}}_{1},{\mathbf{q}}_{\ensuremath{\perp}})$ are the impact factors of particles $a$ and $b$, respectively. The integration is over the two-dimensional transverse momentum of the virtual photons. The important point is that ${\mathcal{I}}^{a} ({\mathcal{I}}^{b})$ does not depend on what particle $b (a)$ is. We have explicitly found the impact factors for the photon (up to ${e}^{4}$) and for the electron, the positron, and the proton (up to ${e}^{2}$). In the case of Delbr\"uck scattering, we have also taken care of all higher-order diagrams with an arbitrary number of photons exchanged between the virtual pair and the proton or nucleus. The coefficient of $s$ in this case can be expressed as the integral of the above-mentioned product ${\mathcal{I}}^{a} {\mathcal{I}}^{b}$ times modified photon propagators. The impact factor therefore appears to express an intrinsic property of a particle. Our result is consistent with neither the most straightforward interpretation of the Regge-pole model nor that of the droplet model. These inconsistencies are closely related to the nonplanar nature of the diagrams under consideration. Our results on Delbr\"uck scattering are also qualitatively different from those of Bethe and Rohrlich based on the impact-parameter approximation.

Passage of charged particles through matter

Abstract: Some commonly used formulas and principal data on the passage of fast charged particles through matter are presented The areas covered include: atomic collision cross sections; stopping power for heavy charged particles; range-energy relations; shell corrections and I-values; straggling of heavy particles; coulomb and multiple scattering, and nuclear interactions; electrons; and mean energy for the formation of an ion pair (GHT)

Multi-regge baryon exchange and central interactions.

Abstract: We find that the double differential cross section for $\mathrm{pp}$ inelastic collisions at high energy can be well reproduced over a range of two decades by a simple version of the multi-Regge model, in which baryon exchange is responsible for large momentum transfers to the final proton. The model is an asymptotic one, and we show predictions at 70 and 200 GeV/c.

Amelioration of divergence difficulties in the theory of weak interactions

Abstract: A new approach to the problem of the singularity of the weak interactions is presented. Its aim is to provide a theoretical interpretation of the extreme smallness of the violation of selection rules associated with the weak-vector-current operator appearing in the conventional Fermi or intermediate-vector-boson interaction Lagrangian. To illustrate what we have in mind, we note that on account of this singular character, the conventional theories have not yet yielded an understanding of the weakness of strangeness and parity violation in hadronic processes and the weakness of semileptonic neutral decays. We begin with an interaction Lagrangian in which the constituents of the conventional weak current (e.g., strangenesschanging, axial-vector, muonic, etc.) are coupled to possibly distinct local vector operators. This is done in such a way that the effective weak interaction between two currents decomposes into two parts, one having the universality of the weak interaction, the other, called diagonal, acting only between a constituent and itself. It is then possible to transfer the singularity of the weak interaction to the diagonal interaction and to impose any desired degree of symmetry upon the singular part of the diagonal interaction. Two realizations of this approach are presented. Both are intermediate-boson theories involving gradient-coupled spin-0 bosons as well as spin-1 bosons. An important consequence of these theories is that, apart from implying a lower bound, the weak interactions give no indication of the magnitude of the diagonal interactions. Thus while the scattering of μ-neutrinos by electrons should be governed by the conventional universality formula, there is no reason to expect universality to hold for the scattering of e-neutrinos by electrons.

Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables

Abstract: It is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products $$\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n $$ ofWightman orJaffe fields.

Particles and Sources

Abstract: It is proposed that the phenomenological theory of particles be based on the source concept, which is abstracted from the physical possibility of creating or annihilating any particle in a suitable collision. The source representation displays both the momentum and the space-time characteristics of particle behavior. Topics discussed include: spin and statistics, charge and the Euclidean postulate, massless particles, and $S{U}_{3}$ and spin. It is emphasized that the source description is logically independent of hypotheses concerning the fundamental nature of particles.

On the low--burnett--kroll theorem for soft-photon emission.

Abstract: SummaryBurnett and Kroll’s extension of Low’s theorem is proved for particles of arbitrary spin.RiassuntoSi prova l’estensione di Burnett e Kroll del teorema di Low per particelle di spin arbitrario.РезюмеДля частиц с произвольным спином доказывается расширение Бурнэ и Кролля для теоремы Лоу.

COVARIANT PHASE-SPACE CALCULATIONS OF n-BODY DECAY AND PRODUCTION PROCESSES.

Abstract: Lorentz-invariant phase-space integrals for decay and production processes involving $n$ particles in the final state---with integrand containing arbitrary invariant functions of momenta of particles---are transformed into simple definite integrals over Mandelstam-like variables. Given the $T$-matrix element squared as a function of scalar products of initial- and final-state particle momenta, the results may be used for the computation of the production cross section, decay rate, energy and momentum spectra, invariant mass spectra, and angular correlations.

Space-time structure in high energy interactions

Abstract: The preceding two talks were motivated by the courageous faith that our present ideas of the continuum and the gravita-tional field extend into the range of elementary particle sizes and far below. Equally interesting to high-energy physicists is the possibilitv that these ideas of saace and time are already at the very edge of their domain and are wrong for shorter distances and times, and that high-energy experiments are a probe through which departure from the classical continuum can be discovered. The present talk is devoted to this alternative. The difficulty is that all our present theoretical work is based on a microscopic continuum and one is faced by the rather formidable problem of redoing all physics in a continuum-free manner. Yet I think those who cope with the conceptual problems of quantum field theory for enough years eventually get sick of the ambiguities and divergencies that seem to derive from the continuum and are driven to seek some way out of this intellectual impasse. I would like to describe a program of this kind that I have been led into after vainly trying to extract some information,; about the small from extremely non-linear field theories. The starting point here also is Riemann, who explicitly poses the question of whether the world is a continuous or a discrete manifold in his famous inaugural lecture. He points out certain philosophical advantages of the discrete manifold, in fact argues for it more strongly than for the continuous. and set devotes his life to the continuous. m Y

Exterior Three-Particle Wave Function

Abstract: For three particles interacting via forces of finite range, it is shown that the wave function interior to the finite volume where all three force ranges overlap completely determines the exterior wave function, provided only the wave functions (half off-shell t matrices) of the isolated two-particle subsystems are also known inside their own range of force. The determination is provided by the solution of a one-variable integral equation with a compact kernel, whose resolvent applied to any parametrization of the interior wave function supplies the equivalent of a phase shift analysis for three-particle final states (exact description of overlapping resonances throughout the Dalitz plot), and (if the interior three-particle fordes are also known) a matrix equation for the interior wave function. (Submitted to Physical Review Letters) * Supported in part by the U. S. Atomic Energy Commission.

Model of the pomeranchuk pole-cut relationship.

Abstract: Using the multiperipheral integral e~uation at zero momentum transfer, we construct a model in which the dynamical interrelation of Regge poles and cuts can be studied. Chief attention is paid to the region near J = 1 in an elastic forward amplitude. A consistent solution is found in which the Pomeranchuk pole appears at J = 1 a, with a ~ 0.01, while the AFS branch point appears at J = 1 2a. To a good approximation the pole residue corresponds to the inelastic part of the total cross section, while the integral over the AFS cut corresponds to the elastic cross section. UCRL-18681 I. TI~TRODUCTION The relationship of Regge cuts and poles remains uncertain, with regard to both relative strength and relative location. Recently it was realized that the multiperipheral integral equation may be able l to shed light on the matters, and we here report a preliminary investigation of the Regge singularities in a forward amplitude, employing the model of Chew and Pignotti 2 (hereafter designated CP) to suggest a simplified kerne~ and inhomogeneous term for the integral equation. The chief emphasis here will be on the region near J = l in an elastic amplitude, but the model can be extended to lower J regions and to inelastic amplitudes. II. THE FACTORIZABLE. MODEL The multiperipheral equation derived in Ref. 3, after projection ' 4 . onto angular momentum J , · · takes the form B\"J' (t I J) a,o J dt B \"J(t,J) G\"J\"J' (t,t',J), a (ILl) with the absorptive part for the forward elastic process ab .... ab given by

Vector meson dominance and high-energy behaviour

Abstract: Assuming that four of the six Mandelstam invariants which describe vector meson production are independent of the vector meson mass λ, we show that vector meson dominance must be written in the helicity frame. We point out that this assumption cannot be justified with kinematical arguments only, and show that it is correct at high energy in various models, including evasive and conspiring Regge-pole exchange, as well as Regge-pole model with absorption. However there remain difficulties with trajectories of the A1 and B type.