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

Thomas D Cohen1

  • 1Department of Physics, University of Maryland, College Park, MD 20742-4111, USA. cohen@physics.umd.edu

Physical Review Letters
|December 20, 2003
PubMed
Summary
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We resolved how chemical potential affects QCD free energy calculations. Our study explains why small chemical potentials do not alter the free energy at zero temperature, contradicting naive expectations.

Area of Science:

  • Quantum Chromodynamics (QCD)
  • High-Energy Physics
  • Theoretical Physics

Background:

  • In quantum chromodynamics (QCD), the free energy is calculated using functional integrals.
  • A chemical potential typically alters the Dirac operator's eigenvalues, naively suggesting a change in free energy.
  • However, phenomenological observations show that small chemical potentials do not affect the free energy at zero temperature.

Purpose of the Study:

  • To reconcile the theoretical expectation with phenomenological observations regarding chemical potential in QCD.
  • To explain the behavior of the QCD free energy at zero temperature with small chemical potentials.
  • To investigate the role of the Dirac operator's spectrum in this phenomenon.

Main Methods:

  • Utilizing a Euclidean space functional integral treatment for QCD.

Related Experiment Videos

  • Analyzing the functional determinant of the Dirac operator, specifically /D+m-mu(f)gamma(0).
  • Studying the spectrum of the operator gamma(0)(/D+m) to understand isospin chemical potential effects.

    • Main Results:

    • The study resolves the discrepancy between theoretical predictions and phenomenological data for QCD free energy at T=0.
    • It is demonstrated how the functional determinant remains unchanged for small chemical potentials, resolving the apparent contradiction.
    • The analysis of the gamma(0)(/D+m) spectrum provides a clear explanation for isospin chemical potential behavior.

    Conclusions:

    • The functional integral treatment of QCD free energy is reconciled with experimental observations at zero temperature.
    • The spectral analysis of the Dirac operator clarifies the role of chemical potential, particularly isospin chemical potential.
    • This work offers a theoretical framework for understanding QCD at finite chemical potentials.