There are numerous kinds of symmetry in nature. As we know, in theoretical physics, symmetry plays important roles. Some are visible and some are hidden. Some are static and some are dynamic. Some belong to simple individual systems and some may be seen in the collective behavior of many body systems. Mathematically, symmetry is expressed as group theory; symmetry of a physical system has been seen as invariance under a group action.
The idea of supersymmetry was originally introduced in relativistic quantum field theories as generalization of Poincare symmetry. In particle physics, supersymmetry (SUSY) is a symmetry that interchanges bosons and fermions. In SUSY theories, every fundamental fermion has a bosonic super partner and vice versa. A SUSY quantum fields theory explain quantum mechanical dynamics and sometimes allows the theory to be solved. If SUSY is applied to the Standard Model of particle physics, the hierarchy problem can be solved. The minimal SUSY Standard Model is one of the best studied candidates for physics beyond the Standard Model. In 2008 the Large Hadron Collider at CERN is scheduled to produce the world’s highest energy collisions and offers the best chance at discovering superparticles in the near future.
In this seminar, I will share and summarize the basic SUSY model which Witten introduced as one dimensional model in 1981. After this SUSY model became a major tool in quantum mechanics and mathematical, statistical, and condensed-matter physics. SUSY is also a successful concept in nuclear and atomic physics. SUSY quantum mechanical system can analyze the properties of the system in an elegant and effective way. In the end of my presentation, I will shortly discuss the relation with Darboux method and Bender and Boettcher’s complex potential which generate real and positive eigenvalue.