Generalized Neumann boundary condition for the scalar field

Abstract

In this paper, we explore the Klein-Gordon field theory in $(D+1)$ dimensions in the presence of a $(D-1)$-dimensional hyperplanar $\delta$-like potential that couples quadratically to the field derivatives. This model effectively generalizes the Neumann boundary condition for the scalar field on the plane, as it reduces to this condition in an appropriate limit of the coupling parameter. Specifically, we calculate the modifications to the Feynman propagator induced by the planar potential and analyze the interaction energy between a stationary point-like source and the potential, obtaining a general and exact expression. We demonstrate that, under certain conditions relating the field mass and the coupling constant to the external potential, the vacuum state becomes unstable, giving rise to a pair-creation phenomenon that resembles the Schwinger effect in quantum electrodynamics.

13 pages, 5 figures

References in corpus (37)

• New Developments in the Casimir Effect
• Dirac materials
• Artificial gauge fields in materials and engineered systems
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Casimir Energies in Light of Quantum Field Theory
• Casimir Energies and Pressures for $\delta$-function Potentials
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• The Casimir Effect for Fermions in One Dimension
• Casimir-Polder effect for a plane with Chern-Simons interaction
• A Neumann Boundary Term for Gravity
• A Green's function approach to the Casimir effect on topological insulators with planar symmetry
• Electromagnetic semitransparent $\delta$-function plate: Casimir interaction energy between parallel infinitesimally thin plates
• Ground states of a Klein-Gordon field with Robin boundary conditions in global anti-de Sitter spacetime
• The Casimir effect: some aspects
• Functional approach to the fermionic Casimir effect
• Maxwell-Chern-Simons Theory With Boundary
• Field theoretic description of partially reflective surfaces
• Interactions between delta-like sources and potentials
• Hertz potentials approach to the dynamical Casimir effect in cylindrical cavities of arbitrary section
• Quantum radiation force on a moving mirror with Dirichlet and Neumann boundary conditions at vacuum, finite temperature and coherent states
• Field theoretic description of electromagnetic boundaries: The Casimir effect between dissimilar mirrors from external potentials
• Neumann Boundary Conditions from Born-Infeld Dynamics
• Vacuum densities for a brane intersecting the AdS boundary
• Neumann Casimir effect: a singular boundary-interaction approach
• Magnetoelectric boundary simulated by a Chern-Simons-like model
• Towards particle creation in a microwave cylindrical cavity
• Local Neumann semitransparent layers: resummation, pair production and duality
• Supersymmetry: Boundary Conditions and Edge States
• Vacuum polarization from confined fermions in 3 + 1 dimensions
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Dirichlet boundary condition for the Lee-Wick-like scalar model
• Generalized boundary conditions in closed cosmologies
• Casimir self-energy of a δ-δ' sphere
• The role of scalar current coupling along surfaces
• Boundary criticality for the Gross-Neveu-Yukawa models
• Finite size effects in the phase transition patterns of coupled scalar field systems