TY - JOUR

T1 - Functional integral approach to semi-relativistic Pauli-Fierz models

AU - Hiroshima, Fumio

N1 - Funding Information:
The author acknowledges support of Grant-in-Aid for Science Research (B) 20340032 , 23340032 , and Challenging Exploratory Research 22654018 from JSPS . He thanks the invitation of the conference The 24th Max Born Symposium at Wroclaw university at 2008, where his research started, and also thanks the hospitality of université de Paris XI, université d'Aix-Marseille-Luminy, université de Rennes I, and Bologna university, where part of this work has been done.

PY - 2014/7/10

Y1 - 2014/7/10

N2 - By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz HamiltoniansH=(p-αA)2+m2-m+V+Hrad in quantum electrodynamics are considered. Here p is the momentum operator, A a quantized radiation field on which an ultraviolet cutoff is imposed, V an external potential, Hrad the free field Hamiltonian and m ≥ 0 describes the mass of electron. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. The Feynman-Kac type formula of e -t H is given. A self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown. All the results are independent of values of coupling constant α, and it is emphasized that m = 0 is included.

AB - By means of functional integrations spectral properties of semi-relativistic Pauli-Fierz HamiltoniansH=(p-αA)2+m2-m+V+Hrad in quantum electrodynamics are considered. Here p is the momentum operator, A a quantized radiation field on which an ultraviolet cutoff is imposed, V an external potential, Hrad the free field Hamiltonian and m ≥ 0 describes the mass of electron. Two self-adjoint extensions of a semi-relativistic Pauli-Fierz Hamiltonian are defined. The Feynman-Kac type formula of e -t H is given. A self-adjointness, a spatial decay of bound states, a Gaussian domination of the ground state and the existence of a measure associated with the ground state are shown. All the results are independent of values of coupling constant α, and it is emphasized that m = 0 is included.

UR - http://www.scopus.com/inward/record.url?scp=84899989507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899989507&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.02.015

DO - 10.1016/j.aim.2014.02.015

M3 - Article

AN - SCOPUS:84899989507

SN - 0001-8708

VL - 259

SP - 784

EP - 840

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -