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

• Main Author: Adams, David H.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: Physical and Mathematical Sciences
• Online Access: https://hdl.handle.net/10356/101088; http://hdl.handle.net/10220/18272
• Institution: Nanyang Technological University

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.