Related papers: Perfect discretization of path integrals
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
The Feynman Propagator of a charged particle confined to an anisotropic Harmonic Oscillator potential and moving in a crossed electromagnetic field is calculated in a conceptually new way. The calculation is based on the expansion of the…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider…
In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
We discuss measures on spaces of unparametrized paths related to the Wiener measure. These measures arise naturally in the study of one-dimensional gravity coupled to scalar fields. Two kinds of discrete approximations are defined, the…
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic…
A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…
This paper presents methodologies to discretize nominal robot paths extracted from 3-D CAD drawings. Behind robot path discretization is the ability to have a robot adjusting the traversed paths so that the contact between robot tool and…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To…
We present a direct path integral derivation of the propagator in the presence of a step potential. The derivation makes use of the Path Decomposition Expansion (PDX), and also of the definition of the propagator as a limit of lattice…