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A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential

David H. Adams
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Abstract

A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential is derived which sheds light on the determinant's dependence on these quantities. This is done via a partial zeta regularisation, formally applying a general formula for the zeta-determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalises the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of general background gauge field; moreover there is no undetermined overall factor. Rigorous versions of this result are obtained in a continuous time--lattice space setting. The determinant expression reduces to a remarkably simple form in the low temperature limit. A program for how to use this to obtain insight into the QCD phase transition at zero temperature and nonzero density is outlined.

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David H. Adams. 2004-04-21. A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential. https://doi.org/10.1103/physrevd.70.045002

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