Related papers: Worldline approach to quantum field theories on fl…
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…
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…
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…
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…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
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…
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.…
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…
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…
We compute the counterterms necessary for the renormalization of the one-loop effective action of massive gravity from a worldline perspective. This is achieved by employing the recently proposed massive $\mathcal{N}=4$ spinning particle…
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 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…
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…
The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
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…
Quantum mechanical models with extended supersymmetry find interesting applications in worldline approaches to relativistic field theories. In this paper we consider one-dimensional nonlinear sigma models with O(N) extended supersymmetry on…
Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In…