Related papers: Perfect discretization of path integrals
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…
$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation.…
In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e.\ the flat spaces $\bbbr^2$ and $\bbbr^3$, the two- and three-dimensional sphere and the two- and three dimensional pseudosphere.…
We present a remarkable discretization of the classical Kepler problem which preserves its trajectories and all integrals of motion. The points of any discrete orbit belong to an appropriate continuous trajectory.
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
This paper presents a time discretization of the robust exact filtering differentiator, a sliding mode differentiator coupled to filter, which provides a suitable approximation to the derivatives of some noisy signals. This proposal takes…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
Recently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields.…
If the diffeomorphism symmetry of general relativity is fully implemented into a path integral quantum theory, the path integral leads to a partition function which is an invariant of smooth manifolds. We comment on the physical…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…