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Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

M. Chaichian·M. N. Mnatsakanova·K. Nishijima·A. Tureanu·Yu. S. Vernov
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Abstract

We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the $\star$-product among the fields, compatible with the twisted Poincaré symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($θ_{0i}=0$), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.

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M. Chaichian, M. N. Mnatsakanova, K. Nishijima, A. Tureanu, Yu. S. Vernov. 2011-03-20. Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. https://doi.org/10.1063/1.3567411

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