Abstract
We investigate, analytically and numerically, the fermion determinant of a new action on a $(1+1)$-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is one-half of that of Kogut and Susskind. In particular, we show that our fermion determinant is real and positive for the U(1) gauge group under specific conditions, which correspond to gauge conditions on the infinite lattice. It is also shown that the determinant is real and positive for the $\mathrm{SU}(N)$ gauge group without any condition.
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