Explicit Diagonalization of Pair Interaction Models
Mathematical Physics
2021-02-10 v3 math.MP
Abstract
We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize a general class of quadratic Hamiltonians. These Hamiltonians describe the pair interaction models. Bogoliubov transformations are constructed algebraically, and the resulting Hamiltonians become the second quantizations of explicit one-particle Hamiltonians. Moreover, an explicit formula for the ground state energies is given. Our method systematically diagonalizes various models of quantum field theory, including a model of a harmonic oscillator coupled to a Bose field and the Pauli-Fierz models in the dipole approximation.
Cite
@article{arxiv.1910.13487,
title = {Explicit Diagonalization of Pair Interaction Models},
author = {Yasumichi Matsuzawa and Itaru Sasaki and Kyosuke Usami},
journal= {arXiv preprint arXiv:1910.13487},
year = {2021}
}
Comments
48 pages