Semiclassical thermodynamics of scalar fields

Abstract

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.

Effective potential in the boundary effective theory formalism

“…( 9) was done in Ref. [6] as an intermediate step to obtain the pressure in the context of a semiclassical approximation. There, it was shown that this quantity can be expressed, for constant φ 0 , in terms of solutions of the equation for small field perturbations propagating on top of the classical solution φ c 1 2…”

“…II, we revisit the usual prescription to obtain the effective action and the effective potential in the functional integral formalism; using the results of Ref. [6], we write the effective potential in terms of the solution of a certain differential equation. In Sec.…”

“…The structure of the paper is as follows: in Section 2, we revisit the usual prescription to obtain the effective action and the effective potential in the functional integral formalism; using the results of Ref. [6], we write the effective potential in terms of the solution of a certain differential equation; in Section 3, we apply the method to the massless λφ 4 /4! theory, and discuss the results for the effective potential; finally, in Section 4, we present our conclusions.…”

Functional density matrix formulation of quantum statistics

“…With this caveat in mind, we will continue to refer to x 0 as a mode of x. 3 With the normalization factor used in Eq. ͑25͒, one has the property: V eff ͑x 0 ͒ → V͑x 0 ͒ when T → ϱ, as follows from Eq.…”

Semiclassical calculation of decay rates

“…In order to integrate (3) over boundary values in the neighborhood of ϕ s (x), we can use the techniques of Ref. [9], which incorporate fluctuations of boundary conditions. We write the boundary field as ϕ(x) = ϕ s (x)+ξ(x), and expand the action up to quadratic order in ξ.…”