Bogoliubov Hamiltonians and one parameter groups of Bogoliubov transformations
Bruneau, L. ; Derezinski, J.
arXiv, 0511069 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-22
Classification:  Mathematical Physics 
@article{0511069,
     author = {Bruneau, L. and Derezinski, J.},
     title = {Bogoliubov Hamiltonians and one parameter groups of Bogoliubov
  transformations},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511069}
}

Bruneau, L.; Derezinski, J. Bogoliubov Hamiltonians and one parameter groups of Bogoliubov
  transformations. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511069/