Year: 1998
Type: article
Abstract: We consider the stochastic limit of the standard non relativistic QED (but our results also hold for the polaron interaction of a particle with a Boson field).Extending the Fock case results of $[\mathrm{A}\mathrm{c}\mathrm{L}\mathrm{u}92]$ , we take the initial state of the field to be a Gibbs state at a given temperature.We show that a new algebra, with commutation relations depending on the temperature and acting on a Hilbert module, emerges.This algebra, that we call the Hot Ree Algebra, generalizes the QED Hilbert module algebra in the sense of $[\mathrm{A}\mathrm{c}\mathrm{L}\mathrm{u}\mathrm{v}_{0}97\mathrm{C}]$ and [Ske96] and therefore also the Ree (or Boltzmannian) algebra.It is interesting to notice that, when the module structure is neglected, the algebra we find is precisely the algebra that was found in the singleton independence central limit theorem of $[\mathrm{A}\mathrm{h}_{0}98\mathrm{a}],$ $[\mathrm{A}\mathrm{h}_{0}98\mathrm{b}]$ .So the present result also gives a natural physical interpretation for that algebra.
Authors: Luigi Accardi, С. В. Козырев, И. В. Волович
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W579756540