相关论文: Heat Kernel and Loop Currents by the Generating Fu…
Earlier in the study of the combinatorial properties of the heat kernel of Laplace operator with covariant derivative diagram technique and matrix formalism were constructed. In particular, this formalism allows you to control the…
We give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schr\"odinger operator with a non-negative and locally bounded potential $V$ such that $V(x) \to \infty$ as $|x| \to \infty$.…
A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…
We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…
The heat generation by an electric current flowing through a quantum dot with the dot containing both electron-electron interaction and electron-phonon interaction, is studied. Using the non-equilibrium Keldysh Green's function method, the…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation,…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…
The leading divergences of the generating functional for Green functions of quark currents between one--nucleon states are calculated with heat kernel techniques. The results allow for a chiral invariant renormalization of all two--nucleon…
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$,…
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
We present a formalism for computing arbitrary multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second…
We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a…
Let us consider a time-dependent differential operator quadratic with respect to the phase variables. Let us consider a multiplication operator defined with the help of a "small" matrix-valued function. Under suitable conditions, we give an…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…
We calculate the divergent part of the one-loop effective action in curved spacetime for a particular class of second-order vector field operators with a degenerate principal part. The principal symbol of these operators has the structure…
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…
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…