Questions about papers on Mathematical Physics

[Jimmy84]

Hi everyone
Im going to start a major in physics next year and I would like to follow mathematical physics afterwards but I lack knowledge about which are the areas of math that contribute the most to the development of physics. For instance I know that differential geometry, functional analysis and abstract algebra specially group theory have deep implications for physics.

I would like to be prepared to write papers and to learn on my own beforehand the most applicable branches of math without having all the knowledge and advantages that a phD students has.

Which books are the best ones to learn mathematical physics?

Which mathematical background do I need in order to learn C algebras?

Which are the areas of math that are the most useful to do research for mathematical physics?

Thanks a lot in advance.

 

[VeeEight]

There are lots of areas of math to study for physics. Some are Functional Analysis, Topology, some Measure Theory, Complex Analysis, Representation Theory, Group Theory and Differential Geometry. The actual uses of these topics becomes apparent when you study more and need to develop more tools.

 

[Kreizhn]

It really depends on what area of physics you plan on entering, as the mathematical aspects vary widely depending on the field. Even pure-mathematical concepts that might not seem like they can be applied to physics have found ways to creep into the study.

For example, it seems unlikely to me that there are many areas of physics that would require an in-depth knowledge of category theory, but I do have a friend working in Quantum Foundations that uses it a fair bit. I think module theory is used in chemical physics but not widely, and hence probably wouldn't be worth studying (other than possibly the repercussions of representation theory).

I cannot speak for things like condensed matter physics and the like, but if you plan on going into relativity theory or quantum mechanics a good short list would be functional analysis, group theory, and differential geometry.

 

[Jimmy84]

It really depends on what area of physics you plan on entering, as the mathematical aspects vary widely depending on the field. Even pure-mathematical concepts that might not seem like they can be applied to physics have found ways to creep into the study.

For example, it seems unlikely to me that there are many areas of physics that would require an in-depth knowledge of category theory, but I do have a friend working in Quantum Foundations that uses it a fair bit. I think module theory is used in chemical physics but not widely, and hence probably wouldn't be worth studying (other than possibly the repercussions of representation theory).

I cannot speak for things like condensed matter physics and the like, but if you plan on going into relativity theory or quantum mechanics a good short list would be functional analysis, group theory, and differential geometry.

Thanks, I am looking perhaps for a field of math that might not be the most difficult or technical but that could allow myself to be able to write papers about it at some point.
I intend to learn on my own some differential and algebraic geometry. But lately I have been considering learning more about functional analysis and measure theory.
Im also interested in the foundations of physics.
What do you guys think about that, is it a realistic enterprise to axiomatize physics ?

Another interesting area of research is constructive quantum field theory. But I can imagine it might be very difficult to find a job in that area.
What is the mathematical background needed in order to figure out that problem?
and does anyone knows good books about mathematical physics to start with?
Thanks.