Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case

TL;DR

This paper explores how quantum space-time deformations, specifically Snyder and GUP models, affect the Fermi-Dirac equation of state and related physical phenomena at finite temperatures.

Contribution

It introduces a generalized framework for the Fermi-Dirac equation of state incorporating finite temperature corrections within deformed quantum phase spaces, analyzing different realizations.

Findings

Three distinct physical regimes identified based on phase space deformations

Deformations significantly alter the equation of state and thermodynamic properties

Physical effects depend on the specific realization of the Snyder model

Abstract

We investigate the impact of the deformed phase space associated with the quantum Snyder space on microphysical systems. The general Fermi-Dirac equation of state and specific corrections to it are derived. We put emphasis on non-relativistic degenerate Fermi gas as well as on the temperature-finite corrections to it. Considering the most general one-parameter family of deformed phase spaces associated with the Snyder model allows us to study whether the modifications arising in physical effects depend on the choice of realization. It turns out that we can distinguish three different cases with radically different physical consequences.