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

Abstract

The 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, , the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, K, a unique parity dominates (conventionally chosen positive), by to 1, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the antifermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we accept, as a fact (consistent with the experimental observation), that fermions (and antifermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.