Wilson Fermion Determinant in Lattice QCD
Abstract
We present a formula for reducing the rank of Wilson fermions from 4 Nc Nx Ny Nz Nt to 4 Nc Nx Ny Nz keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients Cn in the fugacity expansion of the fermion determinant Σn Cn ((μ/T))n, which play an important role in the canonical formulation, using lattice QCD configurations on a 44 lattice. Numerically, |Cn| varies as Nx Ny Nz, and goes easily over the standard numerical range; We give a simple cure for that. The phase of Cn correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.
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