Related papers: Functional determinants by contour integration met…
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…
In this contribution we first summarize how contour integration methods can be used to derive closed formulae for functional determinants of ordinary differential operators. We then generalize our considerations to partial differential…
A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…
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 present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
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…
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…
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…
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…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
Resultants are important special functions used in description of non-linear phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$…
A general method of finding functional determinants is presented that depends on the asymptotic behaviour of the resolvent. Its application to the case of a bounded trihedral corner for which the eigenvalues are known only implicitly is…
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…
We present an overview of the existing methods for computing functional determinants, and outline a possible way forward for Hamiltonians of higher dimensions without radial symmetry.
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 the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bornemann (2011) showed that the condition number of the…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean $AdS_2$ space. More specifically, we consider the ratio of determinants between an operator in the…
In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…