2004/06/03 by Kimball A Milton · 4 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics
paper · doi:10.1088/0305-4470/37/24/014
openalex publication_date 2004/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The Casimir energies and pressures for a massless scalar field associated with δ-function potentials in 1 + 1 and 3 + 1 dimensions are calculated. For parallel plane surfaces, the results are finite, coincide with the pressures associated with Dirichlet planes in the limit of strong coupling, and for weak coupling do not possess a power-series expansion in 1 + 1 dimension. The relation between Casimir energies and Casimir pressures is clarified, and the former are shown to involve surface terms, interpreted as the quantum vacuum energies of the surfaces. The Casimir energy for a δ-function spherical shell in 3 + 1 dimensions has an expression that reduces to the familiar result for a Dirichlet shell in the strong-coupling limit. However, the Casimir energy for finite coupling possesses a logarithmic divergence first appearing in third order in the weak-coupling expansion, which seems unremovable. The corresponding energies and pressures for a derivative of a δ-function potential for the same spherical geometry generalizes the TM contributions of electrodynamics. Cancellation of divergences can occur between the TE (δ-function) and TM (derivative of δ-function) Casimir energies. These results clarify recent discussions in the literature.