Chiral symmetry breaking in lattice gauge theory

Abstract

In the lattice gauge theory, chiral symmetry is naturally spontaneously broken. So we have studied it. After reviewing the lattice gauge theory in the hamiltonian one learn the lattice fermion with species doubling. The species doubling means that lattice fermion always appears a pair with zero net chirality. We have studied Susskind fermion. The chiral symmetry breaking is appeared naturally. Finally, we have studied chiral symmetry breaking in ``naive`` fermion for one color and one flavor. The result is as follow: 1. Chiral symmetry is spontaneously broken. 2. The pseudoscala, pseudoGoldstone particles correspond to antiferromagnetic spin wave excitation of the fermion vacuum. 3. m$^2$ pseudo-Goldstone $\propto$ m fermion $<\bar{4} 4>$