Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I recently read "An Introduction to Supersymmetry in Quantum Mechanical Systems" by T. Wellman (amongst other sources) in an effort to find out what a superpotential actually is and how it relates to the potentials of particles/fields). Here's the link: http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDkQFjAA&url=http%3A%2F%2Fphysics.brown.edu%2Fphysics%2Fundergradpages%2Ftheses%2FSeniorThesis_Wellman.pdf&ei=ulm-UPSCLZOY1AWjwYHYDw&usg=AFQjCNGrg_2jv5NZ7b6k4Fs7er34jgtw3w&sig2=yjQYy1Lf_gZVS-RRefUCsQ

It occurred to me that the Fermionic Hamiltonian and the Bosonic Hamiltonian can be formulated without supersymmetry. On page 13, Wellman expresses these Hamiltonians in terms of the superpotential W in a way that is purely algebraic and doesn't require supersymmetry. In other words we have a bunch of terms that give us the two Hamiltonians; these terms are then simply replaced by W's (see equations 3.2 to 3.9). We only actually get supersymmetry when the separate assertion is made that Q operators exist that transform between our fermionic and bosonic states.

So would it be true to say that non-supersymmetric theories contain superpotentials, W, within their Hamiltonians in the same way that supersymmetric theories do? If this is the case the superpotential is just a useful function that is especially helpfully when we consider supersymmetric theories? I.e. superpotentials exist with or without supersymmetry.

share|improve this question

1 Answer 1

So it seems that I may have found the answer to my own question after consulting Professor Tim Jones of Liverpool University.

It seems that superpotentials mainly serve as a way of writing Lagrangians/Hamiltonians in a more compact way. They're just a form of notation. These Lagrangians/Hamiltonians don't necessarily have to be supersymmetric and we could have our non-supersymmetric theory written in terms of superpotentials (if we wanted to). However, the main application of superpotentials are in supersymmetry, hence the name.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.