High energy modifications of blackbody radiation and dimensional reduction

TL;DR

This paper explores how quantum gravity-inspired modifications to field quantization alter blackbody radiation, leading to a temperature-dependent equation of state and a high-energy dimensional reduction from 4 to 2.5 dimensions.

Contribution

It introduces and analyzes the effects of polymer and deformed Heisenberg quantization on blackbody radiation, revealing a transition in thermodynamic behavior at high temperatures.

Findings

Equation of state shifts from P=ρ/3 to P=2ρ/3 at high T

Stefan-Boltzmann law modifies to ρ ∝ T^{5/2} at high T

Effective spacetime dimensionality reduces to 2.5 at high energy

Abstract

Quantization prescriptions that realize generalized uncertainty relations (GUP) are motivated by quantum gravity arguments that incorporate a fundamental length scale. We apply two such methods, polymer and deformed Heisenberg quantization, to scalar field theory in Fourier space. These alternative quantizations modify the oscillator spectrum for each mode, which in turn affects the blackbody distribution. We find that for a large class of modifications, the equation of state relating pressure $P$ and energy density $\rho$ interpolates between $P=\rho/3$ at low $T$ and $P=2\rho/3$ at high $T$, where $T$ is the temperature. Furthermore, the Stefan-Boltzman law gets modified from $\rho \propto T^{4}$ to $\rho \propto T^{5/2}$ at high temperature. This suggests an effective reduction to 2.5 spacetime dimensions at high energy.