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Scalar field theories in a Lorentz-invariant three-dimensional noncommutative space-time

Shin'ichi Imai·Naoki Sasakura
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Abstract

We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have infrared singularities from the UV/IR mixing. The scalar quantum field theories have the problem that the violation of the momentum conservation from the non-planar diagrams does not vanish even in the commutative limit. A way to obtain an exact translational symmetry by introducing an infinite number of tensor fields is proposed. The translational symmetry transforms local fields into non-local ones in general. We also discuss an analogue of thermodynamics of free scalar field theory in the noncommutative space-time.

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Shin'ichi Imai, Naoki Sasakura. 2000-08-25. Scalar field theories in a Lorentz-invariant three-dimensional noncommutative space-time. https://doi.org/10.1088/1126-6708%2F2000%2F09%2F032

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