Related papers: Worldline Approach to QFT on Manifolds with Bounda…
We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one…
The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the…
The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult…
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation.…
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…
We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…
These two lectures give a pedagogical introduction to the ``string-inspired'' worldline technique for perturbative calculations in quantum field theory. This includes an overview over the present range of its applications. Several examples…
The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of…
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…
An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of…
We present a new method to compute quantum energies in presence of a background field. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Our…
We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study…
We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This…
We revisit the image charge method for the Green's function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
I describe a new method for computing trace anomalies in quantum field theories which makes use of path-integrals for particles moving in curved spaces. After presenting the main ideas of the method, I discuss how it is connected to the…
We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…