We present a first-quantized formulation of the quadratic noncommutative 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 cannot 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).
|Number of pages
|Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
|Published - Feb 14 2002
Bibliographical noteFunding Information:
This work was partly supported by the Russian President's grant 00-15-99296, INTAS grant 01-334 and RFBR grant 01-02-17682-a.
ASJC Scopus subject areas
- Nuclear and High Energy Physics