Yan-Gang Miao, Shao-Jun Zhang
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 nonstandard but has been used in a large amount of literature deduces that a point mass should be described by a Guassian function rather than the usual Dirac delta function. However, we argue the nonstandard quantization procedure by adopting the standard (canonical) quantization procedure 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 nonstandard 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 standard quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor.
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http://arxiv.org/abs/1105.4025
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