High energy modifications of blackbody radiation and dimensional reduction

Understand

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.