open access

https://hdl.handle.net/2115/59115

A New Asymptotic Perturbation Theory with Applications to Models of Massless Quantum Fields

英語

2014-06-01

Springer

Annales Henri Poincare

15(6)

1145-1170

Let H (0) and H (I) be a self-adjoint and a symmetric operator on a complex Hilbert space, respectively, and suppose that H (0) is bounded below and the infimum E (0) of the spectrum of H (0) is a simple eigenvalue of H (0) which is not necessarily isolated. In this paper, we present a new asymptotic perturbation theory for an eigenvalue E(lambda) of the operator satisfying lim (lambda -> 0) E(lambda) = E (0). The point of the theory is in that it covers also the case where E (0) is a non-isolated eigenvalue of H (0). Under a suitable set of assumptions, we derive an asymptotic expansion of E(lambda) up to an arbitrary finite order of lambda as lambda -> 0. We apply the abstract results to a model of massless quantum fields, called the generalized spin-boson model (Arai and Hirokawa in J Funct Anal 151:455-503, 1997) and show that the ground-state energy of the model has asymptotic expansions in the coupling constant lambda as lambda -> 0.

学術雑誌論文

Accepted Manuscript

The final publication is available at link.springer.com

1424-0637

1424-0661