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Rigorous Construction of Liouville Spaces and Thermo Field Dynamics for Bosonic Systems in Mathematics

Authors
Journal
Annals of Physics
0003-4916
Publisher
Elsevier
Publication Date
Volume
223
Issue
1
Identifiers
DOI: 10.1006/aphy.1993.1025
Disciplines
  • Mathematics

Abstract

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.

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