Bogoliubov transformations and fermion condensates in lattice field theories

Understand

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.