Third quantization

Journal Article · Thu Dec 23 04:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3537859· OSTI ID:21511344

Seligman, Thomas H ^[1]; Prosen, Tomaz ^[2]

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1. Instituto de Ciencias Fisicas Universidad Nacional Autonoma de Mexico, Cuernavaca (Mexico)
2. Department of physics, FMF, University of Ljubljana, Ljubljana (Slovenia)

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Some applications, mainly to non-equilibrium steady states, will be mentioned.

• OSTI ID: 21511344
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1323; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
BOSONS
DENSITY
EQUILIBRIUM
FERMIONS
MAGNETIC FIELD CONFIGURATIONS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
OPEN CONFIGURATIONS
PHYSICAL PROPERTIES
QUANTIZATION
SECOND QUANTIZATION
SPACE