Planar field theories with space-dependent noncommutativity

CESAR FOSCO; GONZALO TORROBA

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Lugar: Londres; Año: 2005 vol. 38 p. 3695 - 3707

1751-8113

We study planar noncommutative theories such that the spatial coordinates ${hat x}_1$, ${hat x}_2$ verify a commutation relation of the form: $[{hat x}_1, {hat x}_2] = i theta ({hat x}_1,{hat x}_2)$. Starting from the operatorial representation for dynamical variables in the algebra generated by ${hat x}_1$ and ${hat x}_2$, we introduce a noncommutative product of functions corresponding to a specific operator-ordering prescription. We define derivatives and traces, and use them to construct scalar-field actions. The resulting expressions allow one to consider situations where an expansion in powers of $ heta$ and its derivatives is not necessarily valid. In particular, we study in detail the case when $theta$ vanishes along a linear region. We show that, in that case, a scalar field action generates a boundary term, localized around the line where $theta$ vanishes.