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Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.
Dimensional regularization is a method for regularizing integrals in the evaluation of Feynman diagrams; it assigns values to them that are meromorphic functions of an auxiliary complex parameter d, called the dimension. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension d and spacetime points.
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
The technique was not often taught when Feynman later received his formal education in calculus, but using this technique, Feynman was able to solve otherwise difficult integration problems upon his arrival at graduate school at Princeton University: One thing I never did learn was contour integration. I had learned to do integrals by various ...
This integral is also integrated over the domain of the Feynman parameters. The integral is an isotropic tensor and so can be written as an isotropic tensor without l {\displaystyle l} dependence (but possibly dependent on the dimension d {\displaystyle d} ), multiplied by the integral
Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. Using the well-known observation that = ()!, Julian Schwinger noticed that one may simplify the integral:
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes.In 1947, when Kac and Feynman were both faculty members at Cornell University, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. [1]
Richard Phillips Feynman (/ ˈ f aɪ n m ə n /; May 11, 1918 – February 15, 1988) was an American theoretical physicist.He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and in particle physics, for which he proposed the parton model.