Register

Adv. Query

Q&A (4870)

Reviews (203)

Open problems (47)
Meta (439)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

Interesting topics to research in mathematical physics for undergraduates

1218 views

I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on.

I'm particularity fond of abstract algebra and topology and if possible any topics that involve abstract algebra would/topology/calculus of variations would be especially appreciated

My mentor is involved in work dealing with topological field theories in regards to developments in string theory.

This post has been migrated from (A51.SE)

asked Feb 2, 2012 in Theoretical Physics by Rebel (25 points) [ no revision ]

I think it's better to have a problem in mind rather than the techniques you want to use to solve it. You might not know which techniques should be used ahead of time!

This post has been migrated from (A51.SE)

commented Feb 2, 2012 by Kernel (125 points) [ no revision ]

Cross-posted from Physics.SE http://physics.stackexchange.com/q/20332/2451

This post has been migrated from (A51.SE)

commented Feb 4, 2012 by Qmechanic (3,120 points) [ no revision ]

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

2 Answers

You might want to try to understand what electric and magnetic charges are, and the integrality constraints that they obey. This would not be research, but it involves nice algebraic and differential topology, and would make a good topic for independent study.

This post has been migrated from (A51.SE)

answered Feb 4, 2012 by Eric Zaslow (385 points) [ no revision ]

Your comment on this answer:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

I spent several happy years in entanglement theory during my BSc and MSc days. I was initially interested in the monogamy of entanglement, which was first discussed by Bill Wootters and what I think were two undergraduates -- see http://arxiv.org/abs/quant-ph/9907047. Tests for entanglement include the Peres-Horodecki criterion http://en.wikipedia.org/wiki/Peres%E2%80%93Horodecki_criterion, which is proved by direct application of the Hahn-Banach Theorem (a foundational theorem for Functional Analysis). Three qubits (two-level quantum systems) can be entangled in two completely inequivalent ways: GHZ and W types http://pra.aps.org/abstract/PRA/v62/i6/e062314. These results are all accessible to those with only an undergraduate knowledge in mathematics and quantum physics. The reason is that entanglement is rather amenable to study via the sort of techniques you seem to favour. Entanglement is defined as a lack of separability, which can be tested for in all sorts of sexy ways (the Peres-Horodeki criterion is pretty mouthwatering, and led to the more general idea of developing "entanglement witnesses"). These kinds of buzzwords might be interesting to both you and your mentor.

Good luck!

Edit: good review article for all things entanglement -- http://rmp.aps.org/abstract/RMP/v81/i2/p865_1

This post has been migrated from (A51.SE)

answered Feb 2, 2012 by Kernel (125 points) [ no revision ]

A tangential point - couldn't help noticing that your linked RMP paper has four authors all with the same last name! Is that pure coincidence or is there some systematics to it?

This post has been migrated from (A51.SE)

commented Feb 4, 2012 by Anirbit (585 points) [ no revision ]

Anibit: It's my understanding that they are all family, for example: http://en.wikipedia.org/wiki/Pawe%C5%82_Horodecki

This post has been migrated from (A51.SE)

commented Feb 4, 2012 by Noon Silk (60 points) [ no revision ]

I'm sure it's just a co-incidence... ;-)

This post has been migrated from (A51.SE)

commented Feb 5, 2012 by Kernel (125 points) [ no revision ]

Your comment on this answer:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

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):

Email me at this address if my answer is selected or commented on:

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$\hbar$y$\varnothing$icsOverflow
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).

Please complete the anti-spam verification

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

Your rights

...