Remarks on the canonical quantization of noncommutative theories

TL;DR

This paper examines the canonical quantization of free noncommutative scalar fields, demonstrating that the complex constraint structures can be summed to recover familiar Dirac brackets similar to the commutative case.

Contribution

It provides a closed-form summation of the infinite momenta terms in noncommutative scalar fields, linking the quantization formalism to standard commutative brackets.

Findings

Dirac brackets match commutative case

Infinite momentum terms can be summed explicitly

Quantization methods extend to higher derivative noncommutative theories

Abstract

Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these systems. We study real and complex free noncommutative scalar fields where momenta have an infinite number of terms. We show that these expressions can be summed in a closed way and lead to a set of Dirac brackets which matches the usual corresponding brackets of the commutative case.