Planar field theories with space-dependent noncommutativity

Abstract

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 $\theta$ 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.

21 pages, no figures, LaTeX. v2: Minor typos corrected, comments added. Version to appear in Journal of Physics A

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Cited by in corpus (1)

• Field Theory with Coordinate Dependent Noncommutativity