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Finite Density

  • Mikko Laine
  • Aleksi Vuorinen
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 925)

Abstract

The concept of a system at a finite density or, equivalently, at a finite chemical potential, is introduced. Considering first a complex scalar field, an imaginary-time path integral representation is derived for the partition function. The evaluation of the partition function reveals infrared problems, which are this time related to the phenomenon of Bose-Einstein condensation. A generic tool applicable to any scalar field theory, called the effective potential, is introduced in order to handle this situation. Subsequently the case of a Dirac fermion at a finite chemical potential is discussed. The concept of a susceptibility is introduced. The quark number susceptibility in QCD is evaluated up to second order in the gauge coupling.

Keywords

Noether’s theorem Global symmetry Bose-Einstein condensation Condensate Constrained effective potential Susceptibility 

References

  1. 1.
    G. ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies. Phys. Rev. Lett. 37, 8 (1976)Google Scholar
  2. 2.
    M. D’Onofrio, K. Rummukainen, A. Tranberg, Sphaleron rate in the Minimal Standard Model. Phys. Rev. Lett. 113, 141602 (2014) [1404.3565]Google Scholar
  3. 3.
    J.I. Kapusta, Bose-Einstein condensation, spontaneous symmetry breaking, and gauge theories. Phys. Rev. D 24, 426 (1981)ADSCrossRefGoogle Scholar
  4. 4.
    H.E. Haber, H.A. Weldon, Finite temperature symmetry breaking as Bose-Einstein condensation. Phys. Rev. D 25, 502 (1982)ADSCrossRefGoogle Scholar
  5. 5.
    K.M. Benson, J. Bernstein, S. Dodelson, Phase structure and the effective potential at fixed charge. Phys. Rev. D 44, 2480 (1991)ADSCrossRefGoogle Scholar
  6. 6.
    A. Vuorinen, The Pressure of QCD at finite temperatures and chemical potentials. Phys. Rev. D 68, 054017 (2003) [hep-ph/0305183]Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mikko Laine
    • 1
  • Aleksi Vuorinen
    • 2
  1. 1.AEC, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Department of PhysicsUniversity of HelsinkiHelsinkiFinland

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