Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields

• 成果类型: Article
• 署名作者: Gueneysu, B.; Matte, O.; Moller, J. S.
• 署名单位: Humboldt University of Berlin; Aarhus University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0694-4
• 发表日期: 2017
• 页码: 817-915
• 关键词: pauli-fierz model; quantum electrodynamics; self-adjointness; ground-states; schrodinger semigroups; coupling-constants; hamiltonians

摘要

We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant systems. In particular, we prove the existence of a stochastic flow satisfying the strong Markov property and the Feller property. To this end we employ an explicit solution ansatz. In the matrix-valued case, i.e., if the electron spin is taken into account, it is given by a series of operator-valued time-ordered integrals, whose integrands are factorized into annihilation, preservation, creation, and scalar parts. The Feynman-Kac formula implied by these results is new in the matrix-valued case. Furthermore, we discuss stochastic differential equations and Feynman-Kac representations for an operator-valued integral kernel of the semi-group. As a byproduct we obtain analogous results for Nelson's model.