Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential

TL;DR

This paper investigates how the relationship between positive and negative energy spinors and particles versus antiparticles breaks down for Kogut-Susskind lattice fermions at finite chemical potential, affecting the Fock space construction.

Contribution

It demonstrates that the conventional correspondence of energy signs to particles and antiparticles does not hold for Kogut-Susskind fermions with a specific time derivative, clarifying the underlying structure.

Findings

The energy-spinor correspondence breaks down at finite chemical potential.

Kogut-Susskind fermions exhibit unique Fock space properties.

Comparison with asymmetric time derivative fermions highlights differences.

Abstract

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.