Nonequivalent representations of nuclear algebras of canonical commutation relations: Quantum fields

DOI10.1023/A:1020140632510zbMATH Open1016.81035arXivhep-th/0202038OpenAlexW2165873377MaRDI QIDQ1855319

Yanyan Li

Publication date: 4 February 2003

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Abstract: Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in nonequivalent quantizations of scalar fields.

Full work available at URL: https://arxiv.org/abs/hep-th/0202038

zbMATH Keywords

canonical commutation relationsWick rotationnuclear spaceEuclidean fieldnon-Fock representationsfunctions of rapid decreasenonequivalent quantizations of scalar fields

Mathematics Subject Classification ID

Axiomatic quantum field theory; operator algebras (81T05) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (3)

Nuclear spaces and representations of commutation relations ⋮ Nonstandard representations of the canonical commutation relations ⋮ Infrared singular fields and nonregular representations of canonical commutation relation algebras

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