Related papers: Heat Kernels and Resummations: the Spinor Case
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
In this letter, we prove the existence of resummed expressions for the diagonal of the heat kernel and the effective action of a quantum field which interacts with a scalar or an electromagnetic background. Working in an arbitrary number of…
In a previous paper we have presented a general formalism for computing Feynman diagrams for scalar fields in curved spacetime at any loop order using heat kernel methods. The main technique used is the expansion of the fully off-diagonal…
We adapt the Worldline Formalism to obtain resummed expressions for the effective action and the heat kernel of a quantum scalar field coupled to a Yukawa background. The resummation includes all the invariants built from powers, first…
Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…
The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic at both short and long times, with interestingly different Borel properties for these short and long time expansions. Resummations in terms of incomplete gamma…
We study the strong-field limit of a theory involving a quantum scalar field coupled to a vector background, which can be either an electromagnetic field or a non-gauge field coupled through the first derivative term. Our approach consists…
A short informal overview about recent progress in the calculation of the effective action in quantum gravity is given. I describe briefly the standard heat kernel approach to the calculation of the effective action and discuss the…
A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory with two flavours. A previous result for the one-loop divergences of the pion-nucleon system is confirmed, giving at the same time an…
The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of $N$th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
An asymptotic expansion of the trace of the heat kernel on a cone where the heat coefficients have a delta function behavior at the apex is obtained. It is used to derive the renormalized effective action and total energy of a…
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…
In previous works, we used a so-called deformation formula in order to study, in particular, the Borel summability of the heat kernel of some operators. A goal of this paper is to collect miscellaneous remarks related to these works. Here…
We introduce a new method that exploits the combination of the Heat Kernel (HK) and Background Field Method to compute gauge-invariant and gauge parameter-independent quantities such as the effective potential, anomalous dimensions, and…
We consider the non-local energy-momentum tensor of quantum scalar and spinor fields in $2 w$-dimensional curved spaces. Working to lowest order in the curvature we show that, while the non-local terms proportional to $\Box {\cal R}$, $\Box…
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…
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…
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…