regarding **supersymmetric quantum mechanics**:

By all means you should read and absorb the source of all supersymmetric quantum mechanics, which is still probably the deepest article on this topic, namely the original

This is one fourth of the work that won Witten the Fields medal in 1990.

When I learned this stuff back then, I was very much enchanted by the perspective of spectral geometry (i.e. Connes' spectral triples) that is highlighted in the survey

I'd say if you read that in parallel with Witten, you'll end up with a rather profound understanding of what the deep aspects here are. Because, as you will notice, the topic of susy QM has the tendency to make many people write many rather shallow articles. Stay clear of them and focus on the substantial stuff here.

Speaking of substance, of course the full conceptual impact of supersymmetric QM rests in its relation to index theory and K-theory. You may not need that for your physics project (depends), but for your own education I'd suggest to at least look at the surveys and get the basic idea. This is tremendous stuff.

Finally a fun fact to know -- in particular when somebody quizzes you on applications or is sceptical about the value of supersymmetry -- is that every fermion particle is described by relativistic supersymmetric quantum mechanics *on its worldline*. See here. This is in itself a somewhat trivial fact really, but drastically underappreciated. It is of course directly related to the way that Witten initially bumped into susy QM in the first place, namely by considering the point-particle limit of superstrings.

This post imported from StackExchange Physics at 2014-04-25 13:35 (UCT), posted by SE-user Urs Schreiber