相关论文: Functional determinants via Wronski construction o…
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…
We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…
Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the…
The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by…
We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible we illustrate the general ideas using the Laplacian with…
We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
I present a partly pedagogic discussion of the Gel'fand-Yaglom formula for the functional determinant of a one-dimensional, second order difference operator, in the simplest settings. The formula is a textbook one in discrete…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
A formula relating quotients of determinants of elliptic differential operators sharing their principal symbol, with local boundary conditions, to the corresponding Green function is given.
Based on the Wronski determinant, we propose the construction of linearly independent and orthogonal functions in any Hilbert function space. The method requires only an initial function from the space of functions under consideration, that…
We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to…
General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic…
The formalism which has been developed to give general expressions for the determinants of differential operators is extended to the physically interesting situation where these operators have a zero mode which has been extracted. In the…
We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions…
In this paper we obtain an explicit formula of the parameter dependence of the partial derivatives of the Green's functions related to two-point boundary conditions. Such expression follows as an integral of both kernels times the…
The Gelfand-Yaglom formula relates the regularized determinant of a differential operator to the solution of an initial value problem. Here we develop a generalized Gelfand-Yaglom formula for a Hamiltonian system with Lagrangian boundary…