The technique of decomposing Feynman diagrams at the one loop level into elementary integrals is generalized to the imaginary time Matsubara formalism. The three lowest integrals, containing one, two, and three particle lines, are provided in a form that separates out the real and imaginary parts of these complex functions, according to the input arguments, in a fashion that is suitable for numerical evaluation. The forms given can be evaluated for arbitrary values of temperature, particle mass, particle momenta, and chemical potential.
1996 Academic Press, Inc.
I. INTRODUCTION
The imaginary time Matsubara formalism for Green functions [1] is a venerated method of dealing with problems of finite temperature. This is so because of the fact that Wick's theorem can easily be shown to hold for the Matsubara operators. As such, this method of dealing with finite temperature systems has found wide application, primarily in condensed matter physics (see, e.g. ), but also recently in problems relevant for high energy physics. In particular, it has been recently used in studies of effective QCD Lagrangians (see, e.g. the reviews [4] and [5] and references cited therein), through which an understanding of hot and dense matter is sought [6 10]. However, to date most such studies have often been constrained by specific parameter choices to enable tractability often degenerate particle masses, zero chemical potential or special kinematics are chosen. Furthermore, often only the principal values of these integrals are considered, with the complex nature being completely ignored. An extension of those calculations to physically relevant cases with arbitrary parameters and generalized kinematics, as may be appropriate for example, in calculating Green functions and thereby transport properties in an SU(2) or SU(3) effective model of QCD [8 10], becomes technically extremely complicated. In addition, loop integrals at finite temperature and density are relevant for calculating plasma response functions . It is thus the purpose of this paper to address the technical problems associated with such article no.