On finite 4D quantum field theory in non-commutative geometry

DOI10.1007/BF02099720zbMath0872.58008arXivhep-th/9602115MaRDI QIDQ1357415

P. Prešnajder, Ctirad Klimčík, Harald Grosse

Publication date: 10 June 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9602115

zbMATH Keywords

non-commutative geometry path integral quantization finite 4D quantum field theory

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative differential geometry (46L87) Path integrals in quantum mechanics (81S40) Applications of manifolds of mappings to the sciences (58D30)

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Cites Work