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The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this article we show that the worldline formalism can be applied to this model. We obtain the asymptotic expansion of the heat-kernel corresponding to a scalar field on $mathbb{R}^{d+1}$ in the presence of an arbitrary regular potential and subject to this kind of matching conditions on a flat surface. We also consider two such surfaces and compute their Casimir attraction due to the vacuum fluctuations of a massive scalar field weakly coupled to the corresponding Dirac deltas.
The worldline formalism has been widely used to compute physical quantities in quantum field theory. However, applications of this formalism to quantum fields in the presence of boundaries have been studied only recently. In this article we show how
We present different non-perturbative calculations within the context of Migdals representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar and Proca f
We use the image charge method to compute the trace of the heat kernel for a scalar field on a flat manifold with boundary, representing the trace by means of a worldline path integral and obtain useful non-iterative master formulae for n insertions
In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discret
We study breaking and restoration of supersymmetry in five-dimensional theories by determining the mass spectrum of fermions from their equations of motion. Boundary conditions can be obtained from either the action principle by extremizing an approp