Open AccessOne-loop unitarity of scalar field theories on Poincaré invariant commutative nonassociative spacetimes
Author(s) -
Yuya Sasai,
Naoki Sasakura
Publication year - 2006
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2006/09/046
Subject(s) - noncommutative geometry , unitarity , noncommutative quantum field theory , scalar field , commutative property , quantum field theory , scalar field theory , mathematical physics , feynman diagram , invariant (physics) , theoretical physics , quantization (signal processing) , physics , mathematics , quantum gravity , quantum mechanics , pure mathematics , quantum , algorithm
We study scalar field theories on Poincare invariant commutativenonassociative spacetimes. We compute the one-loop self-energy diagrams in theordinary path integral quantization scheme with Feynman's prescription, andfind that the Cutkosky rule is satisfied. This property is in contrast withthat of noncommutative field theory, since it is known that noncommutativefield theory with space/time noncommutativity violates unitarity in the abovestandard scheme, and the quantization procedure will necessarily becomecomplicated to obtain a sensible Poincare invariant noncommutative fieldtheory. We point out a peculiar feature of the non-locality in ournonassociative field theories, which may explain the property of the unitaritydistinct from noncommutative field theories. Thus commutative nonassociativefield theories seem to contain physically interesting field theories ondeformed spacetimes.Comment: 25 pages, 9 figures ; appendix and references adde
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