Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

Details Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory

2004-02-26

arxiv.org/abs/hep-th/0402212v4

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, version to appear in J. Math. Phys

Scientific paper

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 Poincar\'e symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ($\theta_{0i}=0$), 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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