Results 21 to 30 of about 1,114,315 (242)

A Modified Generalized Analytic Feynman Integral Associated with the Bounded Linear Operator

Axioms, 2022
In this paper, we define a modified and generalized analytic Feynman integral associated with the bounded linear operator on abstract Wiener spaces. We then prove its existence. We also establish some modified and generalized analytic Feynman integration
Hyun Soo Chung
doaj   +1 more source

Evaluation of the general three-loop vacuum Feynman integral [PDF]

, 2016
We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite basis integrals
S. P. Martin, D. G. Robertson
semanticscholar   +1 more source

Reduction to master integrals via intersection numbers and polynomial expansions

Journal of High Energy Physics, 2023
Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly independent master ...
Gaia Fontana, Tiziano Peraro
doaj   +1 more source

Conditional generalized analytic Feynman integrals and a generalized integral equation

International Journal of Mathematics and Mathematical Sciences, 2000
We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals.
Seung Jun Chang, Soon Ja Kang, David Skoug   +2 more
doaj   +1 more source

A Modified Analytic Function Space Feynman Integral and Its Applications

Journal of Function Spaces, 2014
We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances.
Seung Jun Chang, Jae Gil Choi, Hyun Soo Chung   +2 more
doaj   +1 more source

Generalized transforms and convolutions

International Journal of Mathematics and Mathematical Sciences, 1997
In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product.
Timothy Huffman, Chull Park, David Skoug   +2 more
doaj   +1 more source

Continuous-Discrete Path Integral Filtering

Entropy, 2009
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 problem is ...
Bhashyam Balaji
doaj   +1 more source

Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

Journal of High Energy Physics, 2017
We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the ...
Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi   +3 more
doaj   +1 more source

Generalized planar Feynman diagrams: collections

Journal of High Energy Physics, 2020
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates.
Francisco Borges, Freddy Cachazo
doaj   +1 more source

From positive geometries to a coaction on hypergeometric functions

Journal of High Energy Physics, 2020
It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection ...
Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew   +4 more
doaj   +1 more source