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Feynman Diagrams

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Feynman diagrams are important like silicon chip of modern era. Because, these diagrams bring computation to the masses. These diagram are invented by Feynman (1918-1988) in 1948. Freeman J.Dyson systematized these diagrams and become an indispensable operator for performing calculations in modern quantum field theory. They are very important concept in elementary particle phenomena in quantum electrodynamics.

Definition

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Feynman diagrams enable one to find the relevant expressions in an approximate solution to the equations that describe the dynamics of a quantum electrodynamics system. From the conception of the process as a sequence of particle creations and annihilation, one can produce a schematic drawing that relates these creation and annihilation events. The diagram thus obtained can then be translated, element by element into a complex mathematical expression, the evaluation of which yields an observable quantity that characterizes the physical system. 

Rules

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The Feynman rules represent the standard way to do perturbative calculations in quantum gravity. The Feynman rules for calculation of the M matrix depends on the theory used to do the calculation. The basic rules are given first and then the forms required for specific theories. Any diagram will either be a tree diagram (with no loops) or will have one or more closed loops.

  • The diagrams consist of lines and vertices
  • Each internal line represents the propagation of a particular particle from one space-time point to another and the vertices are the points in space time where particles are created or destroyed as described by the interaction Lagrangian of the theory.
  • Label the momenta of each external particle and use energy momentum conservation to determine the four-momentum of each internal line. Tree diagrams have no closed loops and each internal momentum can be fixed in terms of the external momenta. Loop diagrams have momenta which cannot be uniquely specified and these must be integrated over. There will be one undetermined four momentum for each loop.

Feynman Diagrams Explained

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Feynman diagram is nothing but the pictorial representation of mathematical representation of subatomic particles. In simple way, it can be explained as the diagram showing the electromagnetic interactions of subatomic particles. The given figure shows an example of Feynman diagram.

Feynman Diagram
In this figure, two electrons are colliding with each other and the energy exchange is taking place. This exchange of energy through a photon.

Examples

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The examples of Feynman diagram are;

1. Annihilation of electron and positron

The mathematical equation is given as,

Annihilation of Electron and Positron

Electron and positron are combined each other by emitting a photon. Electron emits a photon and positron absorb this photon. While this process \gamma rays are produced in the form of photons. Finally they consumed each other and liberate the energy. The Feynman diagram of this process is,

Example of Feynman Diagrams

Neutron decay and Compton scattering can also represented using Feynman diagram.