Isocliny in spinor space and Wilson fermions

TL;DR

This paper explores the relationship between Clifford algebras and isoclinic subspaces in spinor spaces, introducing isocliny angles to parametrize gamma matrices, and applies this to analyze Dirac traces in lattice quantum field theory with Wilson fermions.

Contribution

It introduces isocliny angles for gamma matrix parametrization and applies this framework to study Dirac traces in Wilson fermions within lattice QFT.

Findings

Clifford algebras relate to isoclinic subspaces and the Hurwitz-Radon problem.

Isocliny angles effectively parametrize gamma matrices.

Application to Dirac traces in Wilson fermions shows practical relevance.

Abstract

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4,0), this parametrization is then applied to the study of Dirac traces occurring in Euclidean lattice quantum field theory within the hopping parameter expansion for Wilson fermions.