TY - JOUR
T1 - Multiplicity of ground states in quantum field models
T2 - Applications of asymptotic fields
AU - Hiroshima, Fumio
N1 - Funding Information:
This work is partially supported by Grant-in-Aid for Science Research (C) 15540191 and 17540181 from MEXT. E-mail address: hiroshima@mpg.setsunan.ac.jp.
PY - 2005/7/15
Y1 - 2005/7/15
N2 - Ground states of Hamiltonian H of quantum field models are investigated. The infimum of the spectrum of H is in the edge of its essential spectrum. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is finite, from which we give an upper bound of the multiplicity of ground states of H. Typical examples are massless GSB models and the Pauli-Fierz model with spin 1/2.
AB - Ground states of Hamiltonian H of quantum field models are investigated. The infimum of the spectrum of H is in the edge of its essential spectrum. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is finite, from which we give an upper bound of the multiplicity of ground states of H. Typical examples are massless GSB models and the Pauli-Fierz model with spin 1/2.
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U2 - 10.1016/j.jfa.2005.03.004
DO - 10.1016/j.jfa.2005.03.004
M3 - Article
AN - SCOPUS:19544363917
SN - 0022-1236
VL - 224
SP - 431
EP - 470
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -