TY - JOUR

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

AU - Hiroshima, Fumio

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

VL - 259

SP - 784

EP - 840

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -