Functional integrals for QCD at nonzero chemical potential and zero density

Details Functional integrals for QCD at nonzero chemical potential and zero density Functional integrals for QCD at nonzero chemical potential and zero density

2003-07-07

arxiv.org/abs/hep-ph/0307089v4

Phys.Rev.Lett. 91 (2003) 222001

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages; typos corrected

Scientific paper

10.1103/PhysRevLett.91.222001

In a Euclidean space functional integral treatment of the free energy of QCD, a chemical potential enters only through the functional determinant of the Dirac operator which for any flavor is $\dslash + m - \mu_f \gamma_0$ (where $\mu_f$ is the chemical potential for the given flavor). Any nonzero $\mu$ alters all of the eigenvalues of the Dirac operator relative to the $\mu=0$ value, leading to a naive expectation that the determinant is altered and which thereby alters the free energy. Phenomenologically, this does not occur at T=0 for sufficiently small $\mu$, in contradiction to this naive expectation. The problem of how to understand this phenomenological behavior in terms functional integrals is solved for the case of an isospin chemical through the study of the spectrum of the operator $\gamma_0 (\dslash + m)$.

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