2003/11/30 by Luiz C. de Albuquerque, R. M. Cavalcanti · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-th
paper · pdf · doi:10.1088/0305-4470/37/27/012
published as J.Phys. A37 (2004) 7039-7050 · 16 pages, 2 figures. Version 2: contains a new section on the renormalization of the two-point Green function in the presence of a flat boundary. Accepted for publication in J. Phys. A
arxiv created 2004/06/01 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work we show how to define the action of a scalar field such that the Robin boundary condition is implemented dynamically, i.e. as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants c 1 and c 2 . Some special cases are discussed; in particular, we show that for some values of c 1 and c 2 the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the λϕ 4 theory subject to the Robin boundary condition on a plate.