Real- and imaginary-time field theory at finite temperature and density

Abstract

This report gives a detailed account of relativistic quantum field theory in the grand canonical ensemble. Three approaches are discussed: traditional Euclidean Matsubara, and two recently developed real-time methods, namely, Minkowskian time-path and thermo field dynamics. The first two formulations are derived in a unified manner from the path-integral representation for the contour-ordered generating functional. Fields with spin and gauge fields, in particular, are included. Zero-temperature renormalizability id shown to imply UV finiteness at any temperature and density. Thermo field dynamics, which is basically an operator theory, is presented in a C ∗-algebraic context. Relevant parts of the HHW formalism of quantum statistical mechanics, and the Tomita-Takesaki theory are explained. The next chapter contains an analysis of the structure and analytic properties of the self-energy and its relation to the full propagator. In this connection the concept of a statistical quasiparticle is briefly described. This is followed by a discussion of thermal WT identities, Results are applied to discuss transversality of the SU( N) gluon polarization tensor. The final chapter deals with the diagrammatic rules for evaluating the pressure and energy density. The energy-momentum tensor is analyzed as a composite operator, and a renormalized virial theorem is established to provide the link with the thermodynamic potential. The pressure of the SU( N) chromoplasma is calculated up to third order.