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Concept# Feynman diagram

Summary

In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other areas of physics, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman di

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This is an overview of a program of stochastic deformation of the mathematical tools of classical mechanics, in the Lagrangian and Hamiltonian approaches. It can also be regarded as a stochastic version of Geometric Mechanics.The main idea is to construct well defined probability measures strongly inspired by Feynman Path integral method in Quantum Mechanics. In contrast with other approaches, this deformation preserves the invariance under time reversal of the underlying classical (conservative) dynamical systems.

2012Gil Badel, Gabriel Francisco Cuomo, Alexander Monin, Riccardo Rattazzi

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U (1) model at the Wilson-Fisher fixed point in D = 4 - epsilon can be computed semiclassically for arbitrary values of lambda n, where lambda is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the U (1) model in 3 - epsilon dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal O(n(0)) contribution to the scaling dimension of large charge operators in 3D CFTs. (C) 2020 Published by Elsevier B.V.

2020We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree- level exchange or contact diagrams. An important example is the computation of the finite coupling 4-point function of the large-N conformal O(N ) model on AdS(3). Remarkably, the re-summation of bubble diagrams is equal to a certain contact diagram: the D1,1,32,32zz function. Another example is a scalar with phi (4) or phi (3) coupling in AdS(3): we compute various 4-point (and higher point) loop bubble diagrams with alternating integer and half- integer scaling dimensions in terms of a finite sum of contact diagrams and tree-level exchange diagrams. The 4-point function with external scaling dimensions differences obeying (12) = 0 and (34) = 1 enjoys significant simplicity which enables us to compute in quite generality. For integer or half-integer scaling dimensions, we show that the M -loop bubble diagram can be written in terms of Lerch transcendent functions of the cross- ratios z and z. Finally, we compute 2-point bulk bubble diagrams with endpoints in the bulk, and the result can be written in terms of Lerch transcendent functions of the AdS chordal distance. We show that the similarity of the latter two computations is not a coincidence, but arises from a vertex identity between the bulk 2-point function and the double-discontinuity of the boundary 4-point function.

2020Related courses (55)

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The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

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Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling and instantons.

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