The coordinate coherent states approach revisited

TL;DR

This paper revisits the coordinate coherent states approach in noncommutative quantum field theory, comparing two quantization methods and their effects on phenomena like the Unruh effect and Hawking radiation.

Contribution

It demonstrates how different quantization procedures influence the description of point particles and the results of quantum effects in noncommutative spacetime.

Findings

Gaussian vs. delta function for point particles depending on quantization

Unruh temperature remains undeformed under first quantization

Hawking temperature is deformed under first quantization

Abstract

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies that the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor.