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Feynman Diagrams

For representing the complex equation governing the interaction of the sub atomic particle, Feynman Diagrams are used. It is easy to understand the diagrammatic representation than analysing the equation. The Feynman Diagram gives a visual explanation of the complex scientific representation.

The Feynman Diagrams have been shown as the space diagrams with the space as one axis and time as another. The space axis is right axis as shown and the time axis is upward axis. Moreover the space axis is similar to x axis and time axis is similar to y axis of the Cartesian co-ordinate system.

Feynman Diagram

In the above diagram, an electron enters and it either emits a photon or absorbs a photon and exits. The photon is shown as the wave in the diagram. The arrow indicates the path taken by the particles. The exchange, emission or absorption of photon occurs at the vertex as shown above.

There are few things to remember when analysing the Feynman diagram. The particles are denoted by the solid lines with the arrow pointing in the direction of travel. The antiparticles on the other hand are also denoted by the solid lines but the arrow in their case is reversed. The virtual particles, like photons, are represented either by the wavy or broken line as shown in the diagram above.

Virtual Photon

Consider the above diagram. Two electrons (or like charges) interacting with each other. The result is the exchange of energy (via a photon particle).

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History of Feynman Diagrams

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The theory of Feynman diagram is proposed and invented by American Physicist Richard Feynman (1918 – 1988). He introduced to world his diagram in 1948 and for his path breaking work he received the Noble prize. According to him these diagrams can be used in quantum physics as well as in solid state theory. Richard was one of the world’s top 10 scientists by a poll conducted in the year 1999. He was member of the team which invented first atomic bomb of Modern world and also the panel member of the team which investigated the space shuttle challenger disaster.

Feynman Rules

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There are certain rules for Feynman diagram. These are as follows:
  1. The charges are conserved irrespective of type of interaction.
  2. Irrespective to the type of interactions, maximum four momentum is conserved.
  3. Irrespective to the type of interactions, the leptons and baryon numbers are conserved.
  4. The integration is represented by a point in the Feynman and is referred as vertex.
  5. The virtual particles, like bosons, are represented by wavy or dotted line.
  6. The bosonic field is represented by wavy line.
  7. The fermionic field is represented by solid line.

Quantum Electrodynamics

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The Quantum Electrodynamics, also termed as QED, is the quantum theory of electrodynamics. This theory explains the interaction between the light and the matter. It is the first and only theory which agrees with both the quantum mechanics and special relativity. The QED has two types of particles fermions (electrons and photons) and gauge bosons (photons).
The QED has three basic features:
  1. The electron can travel from one place and time to another place and time.
  2. The photon can travel from one place and time to another place and time.
  3. The electron can emit or absorbs a photon at a certain place and time.
These Principles can be represented simply by the Feynman diagram as shown below,

Quantum Electrodynamics

As from the diagram it is clear that the electron and photon are the basic particle of QED.

Feynman Diagrams Examples

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The Feynman diagram can helps us in identifying and understanding several nuclear and quantum equations. For example as shown below the Feynman diagram represent the interaction of two electrons with different energies. As can be seen one of them recoils while other gains the momentum due to the acquisition of the photon released in the interaction.
Feynman Diagrams Examples
Due to the force of repulsion the high velocity electron emits the photon and it recoils, while the low velocity electron absorbs the photon and gains the momentum.

2. Another example could be annihilation of electron and positron. This process is given by the equation;

$e^{+} + e^{-}$ →$\gamma$ + $\gamma$ 

This is shown by the diagram as below;

Annihilation of Electron

As seen from the above equation and diagram, when the electron and positron are comes in contact they are attracted towards each other. The electron emits a photon and attracted towards the positron. The electron and positron are combined at the vertex and are consumed by each other, leaving behind only energy in the form of photon.

3. Another example is neutron decay;

$n$ -> $p + e^{-} + anti\ neutrino$

The Feynman diagram of this equation is as shown;
In this one down quark and one up quark of the neutron remains same in the resultant particle i.e. proton, but the other down quarks converted to the up quark by emitting a photon. This photon further converted to the electron and anti neutrino. Thus the equation comes in picture.
This type of quark decay is known as weak decay.

4. Another example of the Feynman diagram is the visualisation of the Compton Scattering. In the Compton scattering the electrons and photons undergoes an elastic scattering. This can be shown below as:
The real electron and photon are combined to form an electron with mass and energy not equal to the real electron. This electron is a virtual electron and is shown in the diagram by the middle line. Due to its unrealistic mass and energy it emits a photon and electron in the process.

The Feynman diagrams are used not only for the equations with the strong electromagnetic and other forces but also for weak forces. They can be drawn for the sub atomic particles like quarks and bosons also.
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