Bogoliubov Hamiltonians and one parameter groups of Bogoliubov transformations
Abstract
On the bosonic Fock space, a family of Bogoliubov transformations corresponding to a strongly continuous one-parameter group of symplectic maps R(t) is considered. Under suitable assumptions on the generator A of this group, which guarantee that the induced representations of CCR are unitarily equivalent for all time t, it is known that the unitary operator U_{nat}(t) which implement this transformation gives a prjective unitary representation of R(t). Under rather general assumptions on the generator A, we prove that the corresponding Bogoliubov transformations can be implemented by a one-parameter group U(t) of unitary operators. The generator of U(t) will be called a Bogoliubov Hamiltonian. We will introduce two kinds of Bogoliubov Hamiltonians (type I and II) and give conditions so that they are well defined.
Keywords
Cite
@article{arxiv.math-ph/0511069,
title = {Bogoliubov Hamiltonians and one parameter groups of Bogoliubov transformations},
author = {L. Bruneau and J. Derezinski},
journal= {arXiv preprint arXiv:math-ph/0511069},
year = {2007}
}