2017/04/12 by Guglielmo Fucci, Klaus Kirsten · 3 citations
Mathematics · Physics and Astronomy · #Action (physics) #Auxiliary field #Boundary value problem #Compactification (mathematics) #Euclidean geometry #Euclidean space #Field (mathematics) #Physics of Superconductivity and Magnetism #Quantum Electrodynamics and Casimir Effect #Quantum many-body systems #Scalar (mathematics) #Scalar field #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.5006657
published in Journal of Mathematical Physics 59(3) (American Institute of Physics) · 22 pages, Latex
arxiv created 2017/04/12 · openalex created_date 2017/04/28 · openalex publication_date 2018/03/01 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05
In this work, we consider the one-loop effective action of a self-interacting λϕ4 field propagating in a D dimensional Euclidean space endowed with d ≤ D compact dimensions. The main purpose of this paper is to compute the corrections to the mass of the field due to the presence of the compactified dimensions. Although the results of the one-loop correction to the mass of a λϕ4 field are very well known for compactified toroidal spaces, where the field obeys periodic boundary conditions, similar results do not appear to be readily available for cases in which the scalar field is subject to Dirichlet and Neumann boundary conditions. We apply the results of the one-loop mass correction to the study of the critical temperature in Ginzburg-Landau models.