A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green's functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as c-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka et al.$---- The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states in a systematic way.A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green's functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as c-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka et al.$---- The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states in a systematic way.

Physical Review CFeb 1, 19916 citations

TWO-BODY CORRELATIONS AND THE ONE-BODY DENSITY MATRIX IN FINITE NUCLEI

A. Polls, Willem H Dickhoff, H. Müther

International Spring Seminar on Nuclear PhysicsApr 1, 20020 citations

Schwinger-Dyson approach to nonequilibrium classical field theory

Krastan B. Blagoev, Fred Cooper, John F. Dawson +1 more

In this paper we discuss a Schwinger-Dyson (SD) approach for determining the time evolution of the unequal time correlation functions of a nonequilibrium classical field theory, where the classical system is described by an initial density matrix at time $t=0.$ We focus on $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ field theory in $1+1$ space-time dimensions where we can perform exact numerical simulations by sampling an ensemble of initial conditions specified by the initial density matrix. We discuss two approaches. The first, the bare vertex approximation (BVA), is based on ignoring vertex corrections to the SD equations in the auxiliary field formalism relevant for $1/N$ expansions. The second approximation is a related approximation made to the SD equations of the original formulation in terms of $\ensuremath{\varphi}$ alone. We compare these SD approximations as well as a Hartree approximation with exact numerical simulations. We find that both approximations based on the SD equations yield good agreement with exact numerical simulations and cure the late time oscillation problem of the Hartree approximation. We also discuss the relationship between the quantum and classical SD equations.In this paper we discuss a Schwinger-Dyson (SD) approach for determining the time evolution of the unequal time correlation functions of a nonequilibrium classical field theory, where the classical system is described by an initial density matrix at time $t=0.$ We focus on $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ field theory in $1+1$ space-time dimensions where we can perform exact numerical simulations by sampling an ensemble of initial conditions specified by the initial density matrix. We discuss two approaches. The first, the bare vertex approximation (BVA), is based on ignoring vertex corrections to the SD equations in the auxiliary field formalism relevant for $1/N$ expansions. The second approximation is a related approximation made to the SD equations of the original formulation in terms of $\ensuremath{\varphi}$ alone. We compare these SD approximations as well as a Hartree approximation with exact numerical simulations. We find that both approximations based on the SD equations yield good agreement with exact numerical simulations and cure the late time oscillation problem of the Hartree approximation. We also discuss the relationship between the quantum and classical SD equations.

arXiv:hep-ph/0106195Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsNov 26, 200167 citations

t=0.

We focus on $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ field theory in

1+1

space-time dimensions where we can perform exact numerical simulations by sampling an ensemble of initial conditions specified by the initial density matrix. We discuss two approaches. The first, the bare vertex approximation (BVA), is based on ignoring vertex corrections to the SD equations in the auxiliary field formalism relevant for

1/N

expansions. The second approximation is a related approximation made to the SD equations of the original formulation in terms of $\ensuremath{\varphi}$ alone. We compare these SD approximations as well as a Hartree approximation with exact numerical simulations. We find that both approximations based on the SD equations yield good agreement with exact numerical simulations and cure the late time oscillation problem of the Hartree approximation. We also discuss the relationship between the quantum and classical SD equations.