Prog. Theor. Phys. Vol. 38 No. 4 (1967) pp. 813-831
Friedrichs-Berezin Transformation and Its Application to the Spectral Analysis of the BCS Reduced Hamiltonian
Physics Laboratory, Faculty of Education, Kobe University, Kobe
*Department of Physics, Kobe University, Kobe
(Received May 31, 1967)
Friedrichs and Berezin's theory on the diagonalization of boson quadratic Hamiltonian is reformulated, and is generalized so as to enable its application to the spectral analysis of Bardeen, Cooper and Schrieffer's reduced Hamiltonian in the theory of superconductivity. The generalization consists in allowing an operator, assumed as strictly positive in the original theory, to have zero and negative eigenvalues with finite multiplicity. It is found that if the operator has only an additional zero eigenvalue the quadratic Hamiltonian remains lower semi-bounded, while it is necessarily unbounded if a negative eigenvalue appears. The BCS reduced Hamiltonian, or rather is equivalent boson Hamiltonian, with a separable interaction falls under the former case. A similar reformulation for fermion quadratic Hamiltonian is also appended.
DOI : 10.1143/PTP.38.813
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