Related papers: Classification of Solvable Feynman Path Integrals
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in…
This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…
One of the key elements of Feynman's formulation of non-relativistic quantum mechanics is a so-called Feynman path integral. It plays an important role in the theory, but it appears as a postulate based on intuition rather than a…
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 present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…
The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus,…
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…
This paper is a continuation of the author's preceding one. In the preceding paper the author has rigorously constructed the Feynman path integral for the Dirac equation in the form of the sum-over-histories, satisfying the superposition…
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…
The article is an overview of the role of graph complexes in the Feynman path integral quantization. The underlying mathematical language is that of PROPs and operads, and their representations. The sum over histories approach, the Feynman…