Related papers: Heat kernel: proper time method, Fock-Schwinger ga…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
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,…
The `problem of time' remains an unresolved issue in all known physical descriptions of the Universe. One aspect of this problem is the conspicuous absence of time in the Wheeler-Dewitt equation, which is the analogue of the Schrodinger…
There are several models for heat conduction - non-Fourier equations - in the literature that are important for various practical problems. These models manifest themselves in partial differential equations, and the application of which…
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…
We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat…
In the presented paper we tackle the problem of the effective field theory in curved spacetime (cEFT) construction. To this end, we propose to use the heat kernel method. After introducing the general formalism based on the well established…
It is studied time dependence of the evolution operator kernel for the Schr\"odinger equation with a help of the Schwinger -- DeWitt expansion. For many of potentials this expansion is divergent. But there were established nontrivial…
The DeWitt expansion of the matrix element $M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle$, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when…
Following Donaldson's oppenness theorem on deforming a conical K\"ahler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical K\"ahler-Ricci Flow exists for…
The Schwinger proper-time method is an effective calculation method, explicitly gauge invariant and nonperturbative. We make use of this method to investigate the radiatively induced Lorentz and CPT-violating effects in quantum…
We propose an innovative isogeometric space-time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of…
This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
We derive an effective classical theory for real-time SU($N$) gauge theories at high temperature. By separating off and integrating out quantum fluctuations we obtain a 3D classical path integral over the initial fields and conjugate…
In the first part of the paper we provide a survey of recent results concerning the problem of pointwise convergence of integral kernels in Feynman path integral, obtained by means of time-frequency analysis techniques. We then focus on…
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…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…
Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the…