Related papers: New Heat Kernel Method in Lifshitz Theories
Nonperturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavors are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective…
The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted dbar-operator in $L^2(C^n)$ for a certain class of weights. The…
In this article, we prove exact estimates for the $W$-invariant Dunkl kernel and heat kernel, for the root system of type $A$ with arbitrary positive multiplicities. We apply the estimates of the $W$-invariant Dunkl heat kernel to compute…
We discuss Weyl anomaly and consistency conditions of local renormalization group in d=1+2 dimensional quantum field theories. We give a classification of the consistency conditions and ambiguities in most generality within the…
We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or…
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…
In this paper, based on the heat kernel technique, we calculate equations of state and thermodynamic quantities for ideal quantum gases in confined space with external potential. Concretely, we provide expressions for equations of state and…
The calculation of heat-kernel coefficients with the classical DeWitt algorithm has been discussed. We present the explicit form of the coefficients up to $h_5$ in the general case and up to $h_7^{min}$ for the minimal parts. The results…
A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength…
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…
In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\sigma_\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as…
In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is based on the newly introduced cutoff energy condition, which…
In this paper, we introduce and motivate the studies of Quantum Weyl Gravity (also known as Conformal Gravity). We discuss some appealing features of this theory both on classical and quantum level. The construction of the quantum theory is…
The off-diagonal heat-kernel expansion of a Laplace operator including a general gauge-connection is computed on a compact manifold without boundary up to third order in the curvatures. These results are used to study the early-time…
We compute the first four heat-kernel coefficients required for the renormalization of Linearized Massive Gravity. We focus on the Fierz-Pauli theory in a curved spacetime, describing the propagation of a massive spin $2$ field in a…
We consider an extension of the Ho\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results…
Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…
The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in $\mathbb{R}^n$, and in particular on the interval, generated by classical differential operators whose eigenfunctions are…