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.
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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 -