Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,862 answers , 20,637 comments
1,470 users with positive rep
502 active unimported users
More ...

Learning about super-symmetric quantum mechanics and integrable systems

+ 5 like - 0 dislike
715 views

I'm an undergraduate interested in theory. I recently asked one of my professors, a physicist in the particle theory group at my school, if he'd be willing to take on an undergraduate for a senior project. He told me to check back in at the end of the quarter, and that he might have a project related to super-symmetric quantum mechanics and integrable systems that may be feasible for me to try out then.

In the meantime, I want to familiarize myself as much as possible with the relevant math and physics so that I can impress him when I ask again. Do any of you have any books/online sources that you recommend I take a look at?

This post imported from StackExchange Physics at 2014-04-25 13:35 (UCT), posted by SE-user BRayhaun
asked Feb 6, 2014 in Theoretical Physics by BRayhaun (25 points) [ no revision ]
retagged Apr 25, 2014
Possible duplicates: physics.stackexchange.com/q/26912 , physics.stackexchange.com/q/30353 and links therein.

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

3 Answers

+ 7 like - 0 dislike

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
answered Feb 7, 2014 by Urs Schreiber (5,805 points) [ no revision ]
+ 4 like - 0 dislike

Integrable supersymmetric models in quantum mechanics (= 1+0-dimensional field theory) are based upon shape invariance. For a comprehensive introduction see

F. Cooper, A. Khare, U. Sukhatme, 
Supersymmetry and quantum mechanics, 
Physics Reports 251 (1995), 267-385. 
http://jensen.thphys.uni-heidelberg.de/~maniatis/LectureAdv/SusyQM.pdf

Another, very recent survey is 

R. Sasaki, Exactly Solvable Quantum Mechanics, arxiv:1411.2703

answered Apr 25, 2014 by Arnold Neumaier (12,385 points) [ revision history ]
edited Nov 28, 2014 by Arnold Neumaier

There's a book I like by Junkers, which emphasizes the stochastic equation aspect. There is an extremely simple Nicolai map, the SUSY-QM is just a stochastic equation in disguise, and this makes all the properties obvious.

The paper is also available on the arXiv: http://arxiv.org/abs/hep-th/9405029

+ 2 like - 0 dislike

For an elementary introduction to supersymmetric quantum mechanics see

Supersymmetry and Quantum Mechanics by Cooper et al. available at

http://arxiv.org/abs/hep-th/9405029

This post imported from StackExchange Physics at 2014-04-25 13:35 (UCT), posted by SE-user just-learning
answered Feb 22, 2014 by just-learning (95 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverfl$\varnothing$w
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...