Related papers: How to (Path-) Integrate by Differentiating

The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…

Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…

The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…

We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…

On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and…

The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend…

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…

It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after…

The main difficulty in solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make…

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

In this paper we introduce new modules over the ring of ponderation functions, so we recover old results in harmonic analysis from the side of ring theory. Moreover, we prove that Laplace transform, Fourier transform and Hankel transform…

Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…

We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…

In this article, a new modified Laplace-Fourier method is developed in order to obtain the solutions of linear neutral delay differential equations. The proposed method provides a more accurate solution than the one provided by the pure…

Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…