Related papers: Heat kernel expansion: user's manual
The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the…
We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat 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…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…
We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…
We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…
In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…
By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…
It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…
We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley-DeWitt coefficients of this decomposition…
The heat kernel expansion for field theory at finite temperature is constructed. It is based on the imaginary time formalism and applies to generic Klein-Gordon operators in flat space-time. Full gauge invariance is manifest at each order…
The trace of the heat kernel and the one-loop effective action for the generic differential operator are calculated to third order in the background curvatures: the Riemann curvature, the commutator curvature and the potential. In the case…
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 give an asymptotic expansion of the relative entropy between the heat kernel $q_Z(t,z,w)$ of a compact Riemannian manifold $Z$ and the normalized Riemannian volume for small values of $t$ and for a fixed element $z\in Z$. We prove that…
The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an oscillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a…
In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to…
Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…