Transfer matrix for Kogut-Susskind fermions in the spin basis

TL;DR

This paper clarifies the differences between spin and flavor basis formulations of Kogut-Susskind fermions with gauge interactions and derives an explicit transfer matrix in the spin basis.

Contribution

It provides the first explicit construction of the transfer matrix in the spin basis for interacting Kogut-Susskind fermions, extending previous free-field results.

Findings

Explicit transfer matrix in the spin basis derived

Demonstrates the transfer matrix generates two lattice unit time translations

Clarifies the difference between spin and flavor basis formulations with gauge fields

Abstract

In the absence of interaction it is well known that the Kogut-Susskind regularizations of fermions in the spin and flavor basis are equivalent to each other. In this paper we clarify the difference between the two formulations in the presence of interaction with gauge fields. We then derive an explicit expression of the transfer matrix in the spin basis by a unitary transformation on that one in the flavor basis which is known. The essential key ingredient is the explicit construction of the fermion Fock space for variables which live on blocks. Therefore the transfer matrix generates time translations of two lattice units.