Diagrammatics of the Dimensionally Reduced Action in phi^4 theory
We describe the Feynman rules for the construction of the Dimensionally Reduced Action (DRA) for a phi^4 field theory, as well as rules for the construction of the connected Green functions and the Dimensionally Reduced Effective Action (DREA), the effective action obtained from the DRA. Two and four-point connected Green functions are calculated to illustrate the application of those rules, and to exhibit the subtraction of UV divergences. As the DRA formalism expands about a background field, instead of the high temperature expansion obtained in the usual dimensional reduced field theory, we derive an expansion that is defined for all range of temperatures. We make a low temperature analysis of the DREA by considering soft modes. In particular, we study the case of near zero mass.