Selfadjointness of a class of multispinboson models with ultraviolet divergences
Abstract
We study a class of quantum Hamiltonian models describing a family of $N$ twolevel systems (spins) coupled with a structured boson field, with a rotatingwave coupling mediated by form factors possibly exhibiting ultraviolet divergences (hence, nonnormalizable). Spinspin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the singlespin case, we provide explicit expressions for the selfadjointness domain and the resolvent operator of such models, both of them carrying an intricate dependence on both the spinfield and spinspin coupling via a family of concatenated propagators. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors via normalizable ones, for example an ultraviolet cutoff.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.10694
 arXiv:
 arXiv:2301.10694
 Bibcode:
 2023arXiv230110694L
 Keywords:

 Mathematical Physics;
 Mathematics  Functional Analysis;
 Quantum Physics;
 81Q10;
 46N50
 EPrint:
 24 pages