Related papers: On equivalent methods for functional determinants
Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, \sigma(x,x'), the square root of the Van Vleck determinant,…
In this paper a new method for computation of higher order corrections to the saddle point approximation of the Feynman path integral is discussed. The saddle point approximation leads to local Schr\"odinger problems around classical…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
We propose the another, in principe nonperturbative, method of the evaluation of the Wiener functional integral for $\phi^4$ term in the action. All infinite summations in the results are proven to be convergent. We finf the "generalized"…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
The functional determinants of the GJMS scalar operators, P_{2k}, on even-dimensional spheres are computed via Barnes multiple gamma functions relying on the numerical availability of the digamma function. For the critical k=d/2 case, it is…
We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
The discrete Gel'fand--Yaglom theorem was studied several years ago. In the present paper, we generalize the discrete Gel'fand--Yaglom method to obtain the determinants of mass matrices which appear current works in particle physics, such…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…
In this paper we have two issues coming from the same background. The first one is to describe a certain ratio of Fredholm determinants of integral operators arising from the Riemann zeta function by using the solution of a single integral…
We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Green equivalence and Green correspondence known in…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
The main objects of our considerations are differential operators generated by a formally selfadjoint differential expression of an even order on the interval $[0,b> (b\leq \infty)$ with operator valued coefficients. We complement and…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by…