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

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.

7 pages. v3: clarification of the sign factor epsilon(A) added; typos corrected; to appear in PRD

References in corpus (6)

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• Fermions on an Interval: Quark and Lepton Masses without a Higgs
• A simplified test of universality in Lattice QCD
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• QCD at high density/temperature
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Cited by in corpus (6)

• Finite-density lattice QCD and sign problem: current status and open problems
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions
• QCD Functional Integrals for Systems with Nonzero Chemical Potential
• Towards extremely dense matter on the lattice
• Low temperature limit of lattice QCD