Spectral analysis of quantum fields using Bogoliubov transformation

Simon N. M. Ruijsenaars

Asao Arai

Elmfors, P., Hiroomi Umezawa

The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the $\\alpha$--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual $2\\times2$ Bogoliubov matrix is extended to a $4\\times4$ matrix including mixing of modes with non--trivial multiparticle correlations. The analysis is carried out for both bosons and fermions.

Jan Dereziński, Christian Gérard

So Katagiri

This paper explores the Bogoliubov transformation's extension to two-mode squeezed states, building on our previous work with Virasoro-squeezing. We establish the Virasoro-Bogoliubov transformation as a non-linear extension of the traditional Bogoliubov transformation, creating non-linear two-mode squeezed states. This research unveils novel quantum states with the potential for innovative insights in various fields of quantum physics.