On second quantization methods applied to classical statistical mechanics

Mario Schönberg

Raoul Gatto

A. Matos Neto

A method of expressing statistical classical r esults in terms of mathematical entities ucually associated to quantum field theoreti - cal treatment of many particle 'systems (Fock space, commutators, field operators, state vector) is discussed. It is developed a linear response theory using the second quantized Liouville equation introduced by sch8nberg. The relationship of this method to that of Prigogine et aZ. is briefly analyzed. The chain of equations and the s pectral represen - tations for the new classical Green's functions a re presented. Gener- alized operators defined on Fock space are dlscussed. It is shown that the correlation functions can be obtained from Green's functions de- fined with generalized operators.

Lukong Cornelius Fai

This chapter introduces and applies the method of second quantization, a technique that underpins the formulation of quantum many-particle theories. Second quantization formalism treats systems of bosons or fermions with a fixed or variable number of particles in a unified way. The chapter reviews the key aspects of this formalism. The formalism of second quantization treats systems of bosons with a fixed or variable number of particles in a unified manner. In many physical processes, the particle number does change. Different quantum operators are expressed most naturally in different representations, which make basis changes an essential issue in quantum physics. Quantum field theory is a universal tool that has applications ranging from atomic, molecular, and particle physics to condensed matter and statistical physics as well as modern quantum chemistry. The fundamental difference between classical and quantum mechanics relates to the concept of indistinguishability of identical particles.

Walter Felipe Wreszinski, G. Scharf