Dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential
Adams, David H.
Date of Issue2004
School of Physical and Mathematical Sciences
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 regularization, formally applying a general formula for the zeta determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalizes the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of a general background gauge field; moreover there is no undetermined overall factor. Rigorous versions of the 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 using this to obtain insight into the QCD phase transition at zero temperature and nonzero density is outlined.
Physical and Mathematical Sciences
Physical review D
© 2004 The American Physical Society. This paper was published in Physical Review D and is made available as an electronic reprint (preprint) with permission of The American Physical Society. The paper can be found at the following official DOI: http://dx.doi.org/10.1103/PhysRevD.70.045002. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.