Covariant perturbation expansion in chiral theories with pions and nucleons

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The Bethe-Goldstone Equation with Singular Interactions: A FulIy OH-ShelI SoIution for the Bounakry Condition Model. R. F. BISHOP. Department of Theoretical Physics, University of Manchester, Manchester Ml3 9PL, England, and Daresbury Laboratory, Daresbury, Warrington WA4 4AD, England. The mutual interaction of a pair of fermions embedded in a many-body system of identical particles when they are excited out of the tiled Fermi sea is studied via the T-matrix or transition amplitude specified by the Bethe-Goldstone (BG) equation. The role of the bare two-body interaction is emphasized, and in particular the consequences are elucidated of whether the potential is “well behaved” (nonsingular) or not. The properties of the BG T-matrix, including generalized orthonormality and completeness relations, are derived both for nonsingular potentials and for singular potentials containing an infinite hard core. General analytic properties are exploited to derive relations that express the fully off-shell BG T-matrix purely in terms of the half-shell amplitude (and the properties of any possible bound states in the medium). The general formalism is illustrated by deriving exact analytic expressions for the fully off-shell BG T-matrices for a pair of particles with equal and opposite momenta interacting via either of two singular model interactions; namely, the pure hard-core interaction and the boundary condition model. Results for both models are expressed in terms of the solution to a simple one-dimensional Fredholm integral equation. The analytic properties of the solutions are discussed and exploited to prove both that they are unique and that they satisfy the various general relations derived. To our knowledge, these results represent the first exact nontrivial solution to the fully off-shell BG equation for any local potential, or singular limiting case thereof. Covariant Perturbation Expansion in Chiral Theories with Pions and N&eons. M. DANIEL, II. Institut fi.ir Theoretische Physik der Universitat Hamburg; AND R. R. HORGAN, Deutsches Elektronen-Synchrotron, DESY, Hamburg. A covariant perturbation scheme is developed to give a coordinate-independent perturbation expansion of the chiral invariant pion model with nucleons. On the mass shell the covariant approach is shown to be equivalent to the standard perturbation theory. A Quantum Theory of Higher Virial Coeficients. T. A. OSBORN AND T. Y. TSANG. Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210. Recently a theory of time-delay phenomena in few-particle scattering has been developed. The results of this theory are used to investigate the quantum virial coefficient problem in the case of Boltzmann statistics. Working within the framework of Faddeev’s time-dependent scattering theory we tind explicit formulas for the higher virial coefficients. One aim of statistical mechanics is to derive all the equilibrium properties of a macroscopic system from the dynamical laws of the constituent particles. Our solutions for the higher virial coefficients prove that the macroscopic properties of a quantum gas are sensitive only to the time-delay aspect of the collision process. The analysis does not restrict the type of interactions between the constituents with the

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