Bogoliubov transformations and fermion condensates in lattice field theories

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.

25 pages

References in corpus (4)

• Foldy-Wouthuysen transformation for relativistic particles in external fields
• Composite boson dominance in relativistic field theories
• A semi-variational approach to QCD at finite temperature and baryon density
• Composite bosons and quasiparticles in a number conserving approach

Cited by in corpus (7)

• Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential
• Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD
• Simple condensation of composite bosons in a number conserving approach to many fermion systems
• Transfer matrix for Kogut-Susskind fermions in the spin basis
• Effective mesonic theory for the 't Hooft model on the lattice
• Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential
• Lattice QCD${}_2$ effective action with Bogoliubov transformations