Functional integrals for QCD at nonzero chemical potential and zero density

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).

Note:

4 pages: typos corrected Report-no: DOE/ER/40762-287: UMDPP 03-058

quantum chromodynamics
potential: chemical
flavor: 2
thermodynamics
functional analysis
partition function

References(22)

Figures(0)

QCD at finite isospin density

D.T. Son
(
- Columbia U. and
- RIKEN BNL
)
,
Misha A. Stephanov
(
- Illinois U., Chicago and
- RIKEN BNL
)

- Phys.Rev.Lett. 86 (2001) 592-595
•
e-Print:
- hep-ph/0005225
•
DOI:
- 10.1103/PhysRevLett.86.592

QCD at finite isospin density: From pion to quark - anti-quark condensation

D.T. Son
(
- Columbia U. and
- RIKEN BNL
)
,
Misha A. Stephanov
(
- Illinois U., Chicago and
- Brookhaven
)

- Phys.Atom.Nucl. 64 (2001) 834-842,
- Yad.Fiz. 64 (2001) 899-907
•
e-Print:
- hep-ph/0011365
•
DOI:
- 10.1134/1.1378872

Imaginary chemical potential and finite fermion density on the lattice

- Phys.Rev.D 59 (1999) 054502
•
e-Print:
- hep-lat/9807039
•
DOI:
- 10.1103/PhysRevD.59.054502

QCD inequalities for the nucleon mass and the free energy of baryonic matter

Thomas D. Cohen
(
- Maryland U.
)

- Phys.Rev.Lett. 91 (2003) 032002
•
e-Print:
- hep-ph/0304024
•
DOI:
- 10.1103/PhysRevLett.91.032002

Matrix model correlation functions and lattice data for the QCD Dirac operator with chemical potential

G. Akemann
(
- Saclay, SPhT
)
,
T. Wettig
(
- Yale U. and
- RIKEN BNL
)

Microscopic correlation functions for the QCD Dirac operator with chemical potential

G. Akemann
(
- Saclay
)

- Phys.Rev.Lett. 89 (2002) 072002
•
e-Print:
- hep-th/0204068
•
DOI:
- 10.1103/PhysRevLett.89.072002

Random matrix theory and chiral symmetry in QCD

J.J.M. Verbaarschot
(
- SUNY, Stony Brook
)
,
T. Wettig
(
- Yale U. and
- RIKEN BNL
)

- Ann.Rev.Nucl.Part.Sci. 50 (2000) 343-410
•
e-Print:
- hep-ph/0003017
•
DOI:
- 10.1146/annurev.nucl.50.1.343

The microscopic spectral density of the QCD Dirac operator

P.H. Damgaard
(
- Bohr Inst.
)
,
J.C. Osborn
(
- SUNY, Stony Brook
)
,
D. Toublan
(
- SUNY, Stony Brook
)
,
J.J.M. Verbaarschot
(
- SUNY, Stony Brook
)

- Nucl.Phys.B 547 (1999) 305-328
•
e-Print:
- hep-th/9811212
•
DOI:
- 10.1016/S0550-3213(99)00094-2

The Spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

- Nucl.Phys.B 560 (1999) 259-282
•
e-Print:
- hep-th/9904199
•
DOI:
- 10.1016/S0550-3213(99)00449-6

Fermion determinants in matrix models of QCD at nonzero chemical potential

Adam Miklos Halasz
(
- SUNY, Stony Brook
)
,
A.D. Jackson
(
- Bohr Inst.
)
,
J.J.M. Verbaarschot
(
- SUNY, Stony Brook
)

- Phys.Rev.D 56 (1997) 5140-5152
•
e-Print:
- hep-lat/9703006
•
DOI:
- 10.1103/PhysRevD.56.5140

NonHermitian random matrix theory and lattice QCD with chemical potential

- Phys.Rev.Lett. 83 (1999) 484-487
•
e-Print:
- hep-lat/9906020
•
DOI:
- 10.1103/PhysRevLett.83.484

Universality of random matrices in the microscopic limit and the Dirac operator spectrum

- Nucl.Phys.B 487 (1997) 721-738
•
e-Print:
- hep-th/9609174
•
DOI:
- 10.1016/S0550-3213(96)00713-4

Random matrix model of QCD at finite density and the nature of the quenched limit

Misha A. Stephanov
(
- Illinois U., Urbana
)

- Phys.Rev.Lett. 76 (1996) 4472-4475
•
e-Print:
- hep-lat/9604003
•
DOI:
- 10.1103/PhysRevLett.76.4472

A Method for simulating chiral fermions on the lattice

David B. Kaplan
(
- UC, San Diego
)

- Phys.Lett.B 288 (1992) 342-347
•
e-Print:
- hep-lat/9206013
•
DOI:
- 10.1016/0370-2693(92)91112-M

Chiral determinant as an overlap of two vacua

- Nucl.Phys.B 412 (1994) 574-606
•
e-Print:
- hep-lat/9307006
•
DOI:
- 10.1016/0550-3213(94)90393-X

Chiral Symmetry Breaking in Confining Theories

Tom Banks
(
- Tel Aviv U.
)
,
A. Casher
(
- Tel Aviv U.
)

- Nucl.Phys.B 169 (1980) 103-125
•
DOI:
- 10.1016/0550-3213(80)90255-2

LATTICE QCD AT FINITE DENSITY

- Phys.Lett.B 215 (1988) 567-572
•
DOI:
- 10.1016/0370-2693(88)91361-5

Simulations with lattice QCD at finite density

I.M. Barbour
(
- Glasgow U.
)
,
Z.A. Sabeur
(
- Glasgow U.
)

- Nucl.Phys.B 342 (1990) 269-278
•
DOI:
- 10.1016/0550-3213(90)90578-2

Complex zeros of the partition function for lattice QCD

I.M. Barbour
(
- Glasgow U.
)
,
A.J. Bell
(
- Glasgow U.
)

- Nucl.Phys.B 372 (1992) 385-402
•
DOI:
- 10.1016/0550-3213(92)90324-5

Canonical ensembles and nonzero density quantum chromodynamics

A. Hasenfratz
(
- Arizona U.
)
,
D. Toussaint
(
- Arizona U.
)

- Nucl.Phys.B 371 (1992) 539-549,
- Nucl. Phys. B371 (1992) 539-549 and Arizona Univ. Tucson - AZ-PH-TH-91-21 (91,rec.Jul.) 15 p
•
DOI:
- 10.1016/0550-3213(92)90247-9

The Critical points of strongly coupled lattice QCD at nonzero chemical potential

Ian M. Barbour
(
- Glasgow U.
)
,
Susan E. Morrison
(
- Glasgow U.
)
,
Elyakum G. Klepfish
(
- King's Coll. London
)
,
John B. Kogut
(
- Illinois U., Urbana
)
,
Maria-Paola Lombardo
(
- Bielefeld, ZIF
)

- Phys.Rev.D 56 (1997) 7063-7072
•
e-Print:
- hep-lat/9705038
•
DOI:
- 10.1103/PhysRevD.56.7063

Random matrices and the convergence of partition function zeros in finite density QCD

Adam Miklos Halasz
(
- Pennsylvania U.
)
,
J.C. Osborn
(
- SUNY, Stony Brook
)
,
Misha A. Stephanov
(
- SUNY, Stony Brook and
- Illinois U., Chicago
)
,
J.J.M. Verbaarschot
(
- SUNY, Stony Brook
)

- Phys.Rev.D 61 (2000) 076005
•
e-Print:
- hep-lat/9908018
•
DOI:
- 10.1103/PhysRevD.61.076005