Corrections to the black body radiation due to minimum-length deformed quantum mechanics

TL;DR

This paper investigates how a minimum-length deformation in quantum mechanics alters the black body radiation spectrum, revealing corrections at different quantization levels with potential implications for early universe physics.

Contribution

It provides an exact first-order calculation of black body radiation corrections due to minimum-length deformed quantum mechanics, highlighting qualitative differences at the second quantization level.

Findings

Corrections are of the same order at both quantization levels.

Second quantization correction has a qualitative difference.

Minimal impact on big-bang nucleosynthesis constraints.

Abstract

Planck spectrum of black body radiation is usually derived by considering of quantized free electromagnetic field at a finite temperature. The minimum-length deformed quantization affects field theory both at the first and second quantization levels. Performing an exact calculation to the first order in deformation parameter, both of the corrections turn out to be of the same order. Nevertheless, the correction at the second quantization level has some qualitative difference, that may be interesting for future study to differentiate between these two sorts of corrections. In itself the correction to the black body radiation seems to be innocuous in light of the big-bang nucleosynthesis whenever the minimum length is less or equal to $10^{-19}$cm.