Geodesic
Hamiltonians of quantum statistics and the model Hamiltonian of the theory of superconductivity
Teoretičeskaâ i matematičeskaâ fizika, Tome 4 (1970) no. 3, pp. 394-411

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An investigation is made of the general Hamiltonian of quantum statistics and the model Hamiltonian of the theory of superconductivity in an infinite volume. The Hamiltonians are given a rigorous mathematical definition as operators in a Hilbert space of sequences of translation-invariant functions. The general Hamiltonian is not symmetric but possesses a real spectrum; the model Hamiltonian is symmetric and its spectrum has a gap between the energy of the ground state and the excited states. 
@article{TMF_1970_4_3_a9,
     author = {D. Ya. Petrina},
     title = {Hamiltonians of quantum statistics and the model {Hamiltonian} of the theory of superconductivity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {394--411},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a9/}
}
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D. Ya. Petrina. Hamiltonians of quantum statistics and the model Hamiltonian of the theory of superconductivity. Teoretičeskaâ i matematičeskaâ fizika, Tome 4 (1970) no. 3, pp. 394-411. http://geodesic.mathdoc.fr/item/TMF_1970_4_3_a9/