Systematics of the electroweak plasma at finite temperature. Part 1

This paper provides a systematic treatment of the finite temperature field theory which will be required for the subsequent calculation in detail (given in the second paper in this series) of the linear response properties of the electroweak plasma at finite temperature at the one-loop level in the Rε gauge. Following a brief summary of the path integral formalism in field theory, the finite temperature theory is introduced with emphasis on the relevant Feynman rules and Matsubara sums. The polarisation tensor for the electroweak plasma is calculated by analysing the appropriate Feynman diagrams. The contributions to the one-loop polarisation tensor are calculated for the tadpole, loop and balloon diagrams in a form suitable for the subsequent investigation of electroweak plasma properties. 32 refs., 2 tabs., ills