Related papers: Local Path Fitting: A New Approach to Variational …
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the…
The gravitational path integral is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential…
A Lagrangian description of the qubit based on a generalization of Schwinger's picture of Quantum Mechanics using the notion of groupoids is presented. In this formalism a Feynman-like computation of its probability amplitudes is done. The…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
We show that, for a class of systems described by a Lagrangian L(x,\dot{x},t) = 1/2\dot{x}^{2} - V(x,t) the propagator can be reduced via Noether's Theorem to a standard path integral multiplied by a phase factor. Using Henstock's…
Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
We study the set of optimal solutions of the dual linear programming formulation of the linear assignment problem (LAP) to propose a method for computing a solution from the relative interior of this set. Assuming that an arbitrary…
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating…
In this paper we provide a variational derivation of the Euler-Poincar\'e equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying…
In this thesis, we develop path integral localization methods that are familiar from topological field theory: the integral over the infinite dimensional integration domain depends only on local data around some finite dimensional…
Within the framework of the path-integral formalism we reinvestigate the different methods of removing the unphysical degrees of freedom from spontanously broken gauge theories. These are: construction of the unitary gauge by gauge fixing;…
We apply the efficient congruencing method to estimate Vinogradov's integral for moments of order 2s, with 1<=s<=k^2-1. Thereby, we show that quasi-diagonal behaviour holds when s=o(k^2), we obtain near-optimal estimates for…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the…