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

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

2000-05-19

arxiv.org/abs/hep-th/0005178v4

JHEP 0009 (2000) 032

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 9 eps figures, LaTeX; references, figures and comments on renormalization added

Scientific paper

10.1088/1126-6708/2000/09/032

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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