Noncommutative field theory in formalism of first quantization

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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).

Original languageEnglish
Pages (from-to)125-130
Number of pages6
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number1-2
StatePublished - Feb 14 2002

Bibliographical note

Funding 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


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