On implementability of Bogoliubov automorphisms and the white noise distribution theory for the Fermion system

TL;DR

This paper investigates the implementability of Bogoliubov automorphisms in Fermion systems using white noise distribution theory, providing a mathematical framework for their continuous linear operator representations.

Contribution

It introduces a method to realize Bogoliubov automorphisms as continuous linear operators on white noise functionals for Fermion systems, utilizing Fock expansion techniques.

Findings

Established conditions for implementability of Bogoliubov automorphisms

Constructed explicit operator representations using Fock expansion

Enhanced mathematical understanding of Fermion system automorphisms

Abstract

In this paper, we consider Bogoliubov automorphisms of CAR algebra and we give implementers as continuous linear operators on the white noise (test or generalized) functionals for the Fermion system with the help of the Fock expansion.