Related papers: Notes on The Feynman Checkerboard Problem
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
We study approximations of Feynman path integrals in finite dimensional spaces and how the approximations determine the propagator.
Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach,…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or…
Suppose we have two nonequivalent but s-equivalent Lagrange functions, the question arises: are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes.
We study a two-loop four-point function with one internal mass. This Feynman integral is one of the simplest Feynman integrals depending on two elliptic curves. We transform the associated differential equation into an $\varepsilon$-form.…
We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states [P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10], describing the functional distribution of particle's…
We study the most elementary model of electron motion introduced by R.Feynman in 1965. It is a game, in which a checker moves on a checkerboard by simple rules, and we count the turnings. The model is also known as one-dimensional quantum…
The purpose of this expository paper is to highlight the starring role of time-frequency analysis techniques in some recent contributions concerning the mathematical theory of Feynman path integrals. We hope to draw the interest of…
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…
Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for non-interacting fermions on a two-dimensional lattice…
Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…
Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schr\"odinger equation are…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
At a fundamental level every measurement process relies on an interaction where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interaction. This results in a…