Bogoliubov transformations and fermion condensates in lattice field theories

TL;DR

This paper explores how generalized Bogoliubov transformations can be used to factorize the transfer matrix in lattice relativistic field theories, aiding in the separation of fermion and antifermion states.

Contribution

It derives conditions for these transformations to effectively separate fermions and antifermions, connecting them to bosonization and Foldy-Wouthuysen transformations.

Findings

Derived conditions for Bogoliubov transformations to factorize the transfer matrix.

Linked the equations to bosonization and energy state separation methods.

Provided solutions under specific conditions for the transformation equations.

Abstract

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian.