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arXiv · hep-th/0104250

Noncommutative field theory in formalism of first quantization

A. Dymarsky
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Abstract

We present a first-quantized formulation of the quadratic non-commutative field theory in the background of abelian (gauge) field. Even in this simple case the Hamiltonian of a propagating particle depends non-trivially on the momentum (since external fields depend on location of the Landau orbit) so that one can not integrate out momentum to obtain a local theory in the second order formalism. The cases of scalar and spinning particles are considered. A representation for exact propagators is found and the result is applied to description of the Schwinger-type processes (pair-production in homogenous external field).

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A. Dymarsky. 2001-04-29. Noncommutative field theory in formalism of first quantization. https://doi.org/10.1016/s0370-2693(02)01166-8

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