TY - JOUR
T1 - Fiber Hamiltonians in non-relativistic quantum electrodynamics
AU - Hiroshima, Fumio
N1 - Funding Information:
I thank Sasaki for his useful comments on the rotation invariance. This work was partially done in “Open Quantum System” at the Ervin Schrödinger Institute (ESI) in March 2005, and “Feynman–Kac Formulas and Their Applications” at the Wolfgang Pauli Institute (WPI) of Uni-versität Vienna in March 2006. The author wishes to thank institutes for their kind hospitality. This work is financially supported by Grant-in-Aid for Science Research (C) 17540181 from JSPS.
PY - 2007/11/1
Y1 - 2007/11/1
N2 - A translation invariant Hamiltonian H of non-relativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum PT:H = underover(∫, Rd, ⊕) H (P) d P, where the self-adjoint fiber Hamiltonian H (P) is defined for arbitrary values of coupling constants. The relationship between rotation invariance of H (P) and polarization vectors is discussed, and functional integral representations of n-point Euclidean Green functions of H (P) are given. From these, applications into the degeneracy of ground states, ground state energy and expectation values of suitable observables with respect to ground states are given.
AB - A translation invariant Hamiltonian H of non-relativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum PT:H = underover(∫, Rd, ⊕) H (P) d P, where the self-adjoint fiber Hamiltonian H (P) is defined for arbitrary values of coupling constants. The relationship between rotation invariance of H (P) and polarization vectors is discussed, and functional integral representations of n-point Euclidean Green functions of H (P) are given. From these, applications into the degeneracy of ground states, ground state energy and expectation values of suitable observables with respect to ground states are given.
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U2 - 10.1016/j.jfa.2007.06.006
DO - 10.1016/j.jfa.2007.06.006
M3 - Article
AN - SCOPUS:34648813559
VL - 252
SP - 314
EP - 355
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -