We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $lambdaphi^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on the solutio
n of the classical equation of motion for the field, and Gaussian fluctuations around it. Our result is non-perturbative and differs from the standard one-loop effective potential for field values larger than $T/sqrt{lambda}$.
We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially non
-perturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with non-trivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $phi_c$, and if we trade free pr
opagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a boundary configur
ation and a zero mode relevant to the discussion of infrared physics. We illustrate our formulation by computing the partition function of an interacting one-dimensional quantum mechanical system at finite temperature from the path-integral representation for the density matrix. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident endpoints, and includes non-vanishing boundary terms. An appropriately modified expansion into Matsubara modes provides a natural separation of the zero-mode physics. This feature may be useful in the treatment of infrared divergences that plague the perturbative approach in thermal field theory.
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around them, provide
non-perturbative information about the theory. In this work, we discuss the calculation of the one-loop effective action from the semiclasssical viewpoint. We intend to use this formalism to obtain an accurate expression for the decay rate of non-static metastable states.
