Supersymmetric gauge theories
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.
A gauge theory is a mathematical framework for analysing gauge symmetries. There are two types of symmetries, viz., global and local. A global symmetry is the symmetry which remains invariant at each point of a manifold (manifold can be either of spacetime coordinates or that of internal quantum numbers). A local symmetry is the symmetry which depends upon the space over which it is defined, and changes with the variation in coordinates. Thus, such symmetry is invariant only locally (i.e., in a neighborhood on the manifold).
Maxwell's equations and quantum electrodynamics are famous examples of gauge theories.
In particle physics, there exist particles with two kinds of particle statistics, bosons and fermions. Bosons carry integer spin values, and are characterized by the ability to have any number of identical bosons occupy a single point in space. They are thus identified with forces. Fermions carry half-integer spin values, and by the Pauli exclusion principle, identical fermions cannot occupy a single position in spacetime. They are identified with matter. Thus, SUSY is considered a strong candidate for the unification of radiation (boson-mediated forces) and matter.
This mechanism works via an operator , known as supersymmetry generator, which acts as follows:
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