A general effective action for quark matter and its application to color superconductivity

  • I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate choices for the projection operators one recovers various well-known effective theories such as the Hard Thermal Loop/ Hard Dense Loop Effective Theories as well as the High Density Effective Theory by Hong and Schaefer. I then apply the effective theory to cold and dense quark matter and show how it can be utilized to simplify the weak-coupling solution of the color-superconducting gap equation. In general, one considers as relevant quark degrees of freedom those within a thin layer of width 2 Lambda_q around the Fermi surface and as relevant gluon degrees of freedom those with 3-momenta less than Lambda_gl. It turns out that it is necessary to choose Lambda_q << Lambda_gl, i.e., scattering of quarks along the Fermi surface is the dominant process. Moreover, this special choice of the two cutoff parameters Lambda_q and Lambda_gl facilitates the power-counting of the numerous contributions in the gap-equation. In addition, it is demonstrated that both the energy and the momentum dependence of the gap function has to be treated self-consistently in order to determine the imaginary part of the gap function. For quarks close to the Fermi surface the imaginary part is calculated explicitly and shown to be of sub-subleading order in the gap equation.

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Author:Philipp Tim ReuterGND
Place of publication:Frankfurt am Main
Referee:Dirk-Hermann RischkeORCiDGND, Jürgen Schaffner-BielichORCiDGND
Advisor:Dirk-Hermann Rischke
Document Type:Doctoral Thesis
Date of Publication (online):2006/09/01
Year of first Publication:2005
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2005/11/30
Release Date:2006/09/01
GND Keyword:Quark-Gluon-Plasma ; Effektive Wirkung ; Supraleitung
Page Number:137
First Page:1
Last Page:137
S.a. http://arxiv.org/abs/nucl-th/0602043
Institutes:Physik / Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):License LogoDeutsches Urheberrecht