Resummation of phi^4 free energy up to an arbitrary order

Abstract

The consistency condition, which guarantees a well organized small-coupling asymptotic expansion for the thermodynamics of massless ${\varphi }^4$-theory, is generalized to any desired order of the perturbative treatment. Based on a strong conjecture about forbidden two-particle reducible diagrams, this condition is derived in terms of functions of four-momentum in place of the common toy mass in previous treatments. It has the form of a set of gap equations and marks the position in the space of these functions at which the free energy is extremal.

Comments: 15 pages, latex, 3 figures using latex, more discussion below (4.14), 3 Ref's added, slight changes in notation