Phase structure of thermal QCD based on the hard thermal loop improved Ladder Dyson-Schwinger equation
Seminar Room 1, Newton Institute
Analyses of the Dyson-Schwinger equation (DSE) have proven to be successful in studying the phase structure of vacuum gauge theories. In the Landau gauge DSE with the ladder kernel for the fermion mass function in the vacuum QED, the fermion wave function renormalization constant is guaranteed to be unity, satisfying the Ward identity. Thus irrespective of the problem of the ladder approximation, the results obtained would be gauge invariant Although in the vacuum case, despite the use of ladder kernel, in the analysis in the Landau gauge the Ward identity is guaranteed to be satisfied, at finite temperature/density there is no such guarantee. In fact, even in the Landau gauge the fermion wave function renormalization constant largely deviates from unity, being not even real. In finite temperature/density QCD/QED, the results obtained from the ladder Dyson-Schwinger equation explicitly violate the Ward identity, thus depend on the gauge, their physical meaning being obscure. In this paper, we study, in the analysis of the HTL resummed improved ladder DS equation for the fermion mass function in thermal QCD, the procedure how we can get the "gauge invariant" solution in the sense it satisfies the Ward identity. The proposed procedure works excellently to obtain a "gauge invariant" solution, at least in the numerical analysis. To get such a solution it is essential that the gauge parameter ? depends on the momentum of the gauge boson. Properties of the "gauge-invariant" solutions are discussed. A theoretical investigation is now underway.