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Progress of Theoretical Physics Supplement

An Extension of TDHF and Boson-Fermion Expansion

Masatoshi Yamamura

Published Jan 1, 1983• 2 citations
Publisher

Abstract

A possible extension of the time-dependent Hartree-Fock theory is given with the aim of obtaining a classical image of the boson-fermion expansion. The extended form can be regarded as a canonical system with constraints and the Dirac quantization reproduces the boson-fermion expansion given by Marshalek.
DOI
10.1143/ptps.74.271

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A classical theory for many-fermion system is presented in the canonical form by introducing the ordinary and the Grassmann variables, the number of which exceeds “apparently” the original one. The basic idea is a translation of a theory proposed by the present authors for the case of the particle-hole pairs to the case of the Hartree-Bogoliubov type pairs. Certain constraints governing the variables are introduced and the double counting in the number of the degrees of freedom concerning the extra variables can be avoided. The quantization is performed with the aid of the Dirac bracket to take account of the constraints. It is shown that final result is completely identical with the compact form of the boson expansion given by Marshalek.
With the use of the ordinary and the Grassmann variables, a classical theory for many-fermion system with particle-hole correlations is presented in a canonical form. This system involves many valence particles/holes in addition to many particle-hole pairs. The particle-hole pairs are assigned as the collective degree of freedom and the others as the independent-particle one. In order to avoid the double counting in the number of the degrees of freedom due to the introduction of the collective variables, certain constraints are introduced. The quantization is performed with the aid of the Dirac theory for canonical system with constraints. It is shown that the result is completely equivalent to that obtained with the use of the boson expansion method by Marshalek.