On the issue of imposing boundary conditions on quantum fields

2003/09/23 by E. Elizalde, E Elizalde · 2 citations
Mathematics · Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #astro-ph #cond-mat #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/36/45/l01

published as J.Phys. A36 (2003) L567 · 13 pages, no figures

arxiv created 2003/09/23 · openalex publication_date 2003/10/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

An interesting example of the deep interrelation between physics and mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments on that and previous analysis are provided here, together with considerations on the results of the purely mathematical zeta-function method, in an attempt at clarifying the issue. Hadamard regularization is invoked in order to fill the gap between the infinities appearing in the QFT renormalized results and the finite values obtained in the literature with other procedures.

Citations

• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• One-loop stress-tensor renormalization in curved background: The relation between ζ-function and point-splitting approaches, and an improved point-splitting procedure
• New Developments in the Casimir Effect
• The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959
• Boundary effects in quantum field theory
• Schrödinger representation and Casimir effect in renormalizable quantum field theory

Cited by

• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique
• Vacuum energy and renormalization on the edge