相关论文: Heat Kernel and Scaling of Gravitational Constants

We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice,…

An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic…

The local momentum space expansion for the real vector field is considered. Using Riemann normal coordinates we obtain an expansion of the Feynman Green function up and including terms that are quadratic in the curvature. The results are…

We study conformal properties of the quantum kinetic equations in curved spacetime. A transformation law for the covariant Wigner function under conformal transformations of a spacetime is derived by using the formalism of tangent bundles.…

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…

Anomalous heat transport observed in low dimensional classical systems is associated to super-diffusive spreading of space-time correlation of the conserved fields in the system. This leads to non-local linear response relation between the…

In a first step we will provide arguments for the understanding of quantum space-time (QST), that means, the microscopic substructure which is assumed to underly ordinary smooth classical space-time, as a thermal system at each…

In this paper we will present very recent results obtained in the ambit of quantum electrodynamics in curved spacetime. We utilize a newly developed non-perturbative heat kernel asymptotic expansion on homogeneous Abelian bundles over…

The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…

After establishing the positivity constraint and spin content of the theory for gravitons interacting with a necessarily, and \textit{a priori}, \textit{non}-conserved external energy-momentum tensor, the expectation value formalism of the…

This article shows that under locally uniformly integral bounds of the negative part of Ricci curvature the heat kernel admits a Gaussian upper bound for small times. This provides general assumptions on the geometry of a manifold such that…

Generalizing to relativistic exponential scaling and using the theory of noise from quantum fluctuations, it has been shown that one vacuum (Rindler, Hartle-Hawking, or Gibbons-Hawking for the cases of the uniformly accelerated detector,…

Finite temperature corrections to the effective potential and the energy-momentum tensor of a scalar field are computed in a perturbed Minkoswki space-time. We consider the explicit mode decomposition of the field in the perturbed geometry…

Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…

This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic…

We analyze the renormalized stress-energy tensor (RSET) of a massless quantum scalar field in time-dependent gravitational backgrounds. Starting from its formal expression obtained within the covariant perturbative expansion to lowest order…

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…

The real physics meaning of constant k in the Robertson-Walker metric is discussed when scalar factor R(t) is relative to time. Based on the curvature formula of the Riemannian geometry strictly, the spatial curvature of the R-W metric is…

Can you hear the shape of Liouville quantum gravity? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the $n$-th eigenvalue grows linearly with $n$, with the proportionality constant given by the Liouville area of the…