Search results
Results from the WOW.Com Content Network
This version of Phenomena is often referred to as the "integral cut". [24] A shorter version of the film was prepared for international release that had a 110-minute running time. [24] This version of the film only cuts out minor material from the "integral cut" with most being a few frames at the end and beginning of shots. [24]
One-loop diagrams are usually computed as the integral over one independent momentum that can "run in the cycle". The Casimir effect , Hawking radiation and Lamb shift are examples of phenomena whose existence can be implied using one-loop Feynman diagrams, especially the well-known "triangle diagram":
The remaining two half-lines in the two X s can be linked to each other in two ways, so that the total number of ways to form the diagram is 4 × 3 × 4 × 3 × 2 × 2, while the denominator is 4! × 4! × 2!. The total symmetry factor is 2, and the contribution of this diagram is divided by 2.
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 1 A n = 1 ( n − 1 ) ! ∫ 0 ∞ d u u n − 1 e − u A , {\displaystyle {\frac {1}{A^{n}}}={\frac {1}{(n-1)!}}\int _{0}^{\infty }du\,u^{n-1}e^{-uA},}
Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions.
QED was designed to be a popular science book, written in a witty style, and containing just enough quantum-mechanical mathematics to allow the solving of very basic problems in quantum electrodynamics by an educated lay audience. It is unusual for a popular science book in the level of mathematical detail it goes into, actually allowing the ...
For example in QED, the tensor indices of the integral may be contracted with Gamma matrices, and identities involving these are needed to evaluate the integral. In QCD, there may be additional Lie algebra factors, such as the quadratic Casimir of the adjoint representation as well as of any representations that matter (scalar or spinor fields ...
In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini [1] as well as – independently and more comprehensively [2] – by 't Hooft and Veltman [3] for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number ...