Relativistic dynamics compels a thermalized Fermi gas to a unique intrinsic parity eigenstate

TL;DR

This paper investigates how relativistic effects and temperature influence the intrinsic parity and helicity correlations in a Fermi gas, revealing a transition from mixed to definite parity states as temperature decreases.

Contribution

It introduces a quantum information framework to analyze spin-parity correlations in a relativistic Fermi gas, highlighting temperature-dependent parity dominance.

Findings

At high temperatures, fermions have no definite intrinsic parity, with a 50-50 correlation with helicity.

At low temperatures (~3 K), a unique intrinsic parity dominates, with a ratio of 10^20 to 1.

Quantum correlations decohere as temperature decreases, leading to a definite parity state.

Abstract

Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two qubits of information: helicity and intrinsic parity. We show that the density matrix for a gas of free fermions, in thermal equilibrium, correlates helicity and intrinsic parity. Our results introduce the basic elements for discussing the spin-parity correlation for a Fermi gas: (1) at the ultra-relativistic domains, when the temperature is quite high, $T > 10^{10}\ K$, the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, $T \approx 3 \ K$, a unique parity dominates (conventionally chosen positive), by $10^{20}$ to $1$, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the anti-fermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we do accept, as a fact (consistent with the experimental observation), that fermions (and anti-fermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.