What is Supersymmetry and Supermath ?

In a nutshell supermath is the math of supersymmetry. In truth it is much more than just that, but lets start with supersymmetry.

This begs the question, what is supersymmetry ? Supersymmetry is a radical new hypothetical symmetry which is currently popular among modern theoretical physicists. In particular supersymmetry (or SUSY for short) proposes that there is a fundamental balance between fermions and bosons. Essentially, solid objects are built from fermions. Bosons in contrast are not solid, they are said to propogate the known forces. For example, light is made of photons and it propogates the electromagnetic force. The symmetry of SUSY involves and exchange of bosons with fermions. In particular, if we were to consider a physical system with a single boson and non-trivial SUSY then there would automatically be a fermion in the system. It is a logical consequence of SUSY.

If you like analogies, SUSY is like P.A.M. Dirac's discovery of antiparticles back in early 20th century. Before that we just had particles, after that if we found most any particle then by a certain line of theoretical reasoning there must exist a corresponding antiparticle. So Dirac's hypothesis doubled the size of physic's domain. SUSY proposes something similar, for every boson and fermion there must be a corresponding superpartner fermion or boson. For technical reasons the known particles can not be superpartners. Consequently it is the hope of many people in the physics community that the new Large Hadron Collider (LHC) will discover some of these new particles predicted by SUSY. I should point out that this is mostly speculation at this point, we do not have any experimental confirmation of SUSY.

Supersymmetry is simply an appealing theoretical construct. I suspect that even if the LHC does not find SUSY the idea will continue to populate theoretical physics. People accept it now because of the theoretical puzzles it solves, that will not change if the LHC does not find SUSY. The tricky thing is that SUSY is a broken symmetry at the energy levels of our day to day life. In order to see SUSY revealed it will be necessary to probe much higher energies. The hypothesis that the LHC will reach sufficient energy to observe SUSY is not inescapable. In fact, some theorists even now argue we ought not see signatures of SUSY until a higher energy is reached in experiments.

The chronological history of SUSY is fairly short. The idea is not much older than myself. Most of the big ideas were set out by theoretical physicists in the mid to late 1970's. There are a number of fairly well written, but typically dense, introductory texts on the subject. If you'd like I could point you towards a good starting point given your background. Just stop by office hours or send me an email.



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Last Modified: 7-16-08