Application of second quantization methods to the classical statistical mechanics

A. Matos Neto

Raoul Gatto

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.

N N Bogolubov, N N Bogolubov, Jr.

Problem Non Ideal Bose Gas, Superfluidity and Fundamental Aspects of Quasiaverages Application Quasiaverages in the Theory of Superconductivity Correlations Weakening and Theorems on Singularities of the Type 1/Q2 Some Remarks on the Ergodic Theory (and Real Example From Statistical Mechanics Where the Usual Ergodic Conditions Not Satisfed) Presented Revised (More Simplified Version) Method of Second Quantized Representation for Wave Functions of Boson and Fermion Particles and Dynamical Operators.

Walter Felipe Wreszinski, G. Scharf