Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

Details Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

2003-08-06

arxiv.org/abs/hep-th/0308043v1

JHEP 0401 (2004) 017

Physics

High Energy Physics

High Energy Physics - Theory

70 pages AMSTeX

Scientific paper

10.1088/1126-6708/2004/01/017

We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra.

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