Rigorous construction of liouville spaces and thermo field dynamics for bosonic systems in mathematics

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Abstract

We clarify the mathematical difficulty when for bosonic systems (i.e., unbounded operators) we rigorously construct a Liouville space, in which a Liouville operator acts, associated with a Hamiltonian. Including unbounded and non-quasi-free cases. We give thermo field dynamics as an expression equivalent to the Liouville space and operator. We investigate the mathematical properties of them, and thus we clarify the mathematical properties of the thermal state.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalAnnals of Physics
Volume223
Issue number1
DOIs
Publication statusPublished - Apr 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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