Finite Size Effects in Thermal Field Theory

Abstract

We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary surfaces (two parallel hyperplanes), which break translational symmetry. In order to identify the singular parts of the one-loop two-point and four-point Schwinger functions, we use a combination of dimensional and zeta-function analytic regularization procedures. The infinities which occur in both the regularized one-loop two-point and four-point Schwinger functions fall into two distinct classes: local divergences that could be renormalized with the introduction of the usual bulk counterterms, and surface divergences that demand countertems concentrated on the boundaries. We present the detailed form of the surface divergences and discuss different strategies that one can assume to solve the problem of the surface divergences. We also briefly mention how to overcome the difficulties generated by infrared divergences in the case of Neumann-Neumann boundary conditions.

31 pages, latex, to appear in J. Math. Phys

References in corpus (14)

• New Developments in the Casimir Effect
• Effective Field Theory Approach to High-Temperature Thermodynamics
• Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories
• On the Convergence of Perturbative QCD at High Temperature
• Foam Diagram Summation at Finite Temperature
• Vacuum Energy Density near Fluctuating Boundaries
• Zero-point energy of massless scalar fields in the presence of soft and semihard boundaries in D dimensions
• Boundary dependence of the coupling constant and the mass in the vector N-component $(\lambda {\varphi }^4{)}_D$ theory
• One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes
• Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• The thermal coupling constant and the gap equation in the $\lambda {\varphi }_D^4$ model
• Strong-coupling expansion of chiral models
• One-loop dimensional reduction of the linear sigma model

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