The Green’s function method in the Kadanoff-Baym version provides a basic theory for nuclear dynamics which is applicable also to nonzero temperature and to nonequilibrium systems. At the same time, it maintains the basic many-body techniques of the Brueckner theory that makes reasonable a comparison of the numerical results of the two methods for equilibrium systems. The correct approximation to the spectral function which takes into account the widths of energy levels is offered and discussed, and the comparison of the values of binding energy in the two methods is produced. 1. Introduction The only microscopic theory which is capable of describing dynamical and statistical properties of quantum many-body systems in a comprehensive way is the Green’s function approach initiated by Martin and Schwinger and later developed by Kadanoff and Baym [1, 2] with specific application to nuclear matter in [3–6]. Traditional many-body theories of nuclei such as Brueckner’s are based on a quasiparticle picture ab initio neglecting the widths of the energy levels associated with the strong interactions when calculating the binding energy. In its original form, the Brueckner theory only considers particle propagation in intermediate states by defining a two-body reaction matrix of “effective” interaction or similarly defined objects [3]. Different approximations to the spectral functions in the Kadanoff-Baym method established a link between the Brueckner and the Green’s function theories [3–6]. Similar approximations to the spectral functions and kinetic equations were considered also in [7–9]. Unfortunately, all the approximations offered in [3–9] turned to be unsatisfactory as it was shown in [10]. The purpose of this paper is to generalize the results of [10] concerning the spectral function and to clarify some of the quantitative relations between the two methods in nuclear physics on the basis of these results. We show that the self-consistent approximations in the two theories lead to very close results, although numerical calculations of the binding energy are still limited by our limited knowledge of nuclear forces and many-body effects. 2. Spectral Functions of the Particle and Quasiparticle States in the Kadanoff-Baym Approach The KB formalism results in the following general expression for a one-particle spectral function for a system in equilibrium state [1, 2, 10]: where and is a one-particle energy in the Hartree-Fock approximation. Real and imaginary parts of the correlation self-energy function are related through the Hilbert transform Here, refers
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