Abstract:
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.
Citation:
D. Ya. Petrina, “Hamiltonians of quantum statistics and the model Hamiltonian of the theory of superconductivity”, TMF, 4:3 (1970), 394–411; Theoret. and Math. Phys., 4:2 (1970), 916–928
\Bibitem{Pet70}
\by D.~Ya.~Petrina
\paper Hamiltonians of quantum statistics and the model Hamiltonian of the theory of superconductivity
\jour TMF
\yr 1970
\vol 4
\issue 3
\pages 394--411
\mathnet{http://mi.mathnet.ru/tmf4162}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=462402}
\zmath{https://zbmath.org/?q=an:0201.58503}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 4
\issue 2
\pages 916--928
\crossref{https://doi.org/10.1007/BF01038305}
Linking options:
https://www.mathnet.ru/eng/tmf4162
https://www.mathnet.ru/eng/tmf/v4/i3/p394
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