Noncommutative field theory in formalism of first quantization

A. Ya Dymarsky

doi:10.1016/S0370-2693(02)01166-8

Noncommutative field theory in formalism of first quantization

A. Ya Dymarsky

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 language	English
Pages (from-to)	125-130
Number of pages	6
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	527
Issue number	1-2
DOIs	https://doi.org/10.1016/S0370-2693(02)01166-8
State	Published - 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.

Funding

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.

Funders	Funder number
INTAS, Belgium	01-334
Russian Foundation for Basic Research	01-02-17682-a

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/S0370-2693(02)01166-8

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Y1 - 2002/2/14

N2 - 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).

AB - 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).

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-2

ER -

Noncommutative field theory in formalism of first quantization

Abstract

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