Noncommutative field theory in formalism of first quantization
arXiv:hep-th/0104250 · doi:10.1016/S0370-2693(02)01166-8
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).
LaTeX, 6 pages