Local Neumann semitransparent layers: resummation, pair production and duality

Abstract

We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat-kernel to all order in a homogeneous background and to quadratic order in perturbations, giving a closed expression for the corresponding effective action in $D=4$. In the dynamical case, we analyze the pair production caused by a harmonic perturbation and by a Sauter pulse. Notably, we prove the existence of a strong/weak duality that links this Neumann field theory to the analogue Dirichlet one.

32 pages, 2 figures

References in corpus (19)

• Dynamically assisted Schwinger mechanism
• Current status of the Dynamical Casimir Effect
• Worldline Instantons II: The Fluctuation Prefactor
• Worldline algorithms for Casimir configurations
• Roughness correction to the Casimir force : Beyond the Proximity Force Approximation
• Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Quantum dissipative effects in moving mirrors: a functional approach
• Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
• Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response
• Čerenkov radiation in vacuum from a superluminal grating
• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Semi-transparent Boundary Conditions in the Worldline Formalism
• Van der Waals Anomaly
• Duality between weak and strong interactions in quantum gases
• Non-perturbative Quantum Propagators in Bounded Spaces
• Scalar Field with Robin Boundary Conditions in the Worldline Formalism
• Vacuum energy density and pressure inside a soft wall
• Casimir energy due to inhomogeneous thin plates

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• Worldline approach for spinor fields in manifolds with boundaries
• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Monte Carlo generation of localised particle trajectories
• Generalized Neumann boundary condition for the scalar field