Constructive Quantum Field Theory and Euro grad school

[JasonJo]

I will be applying for grad school this Winter, but from January 2009-September 2009, I will be done with any course work and will not have any money to commute to my school to continue to do research. So I figured it would be a good opportunity to go further in my mathematics and physics studies.

In graduate school I really want to focus on mathematical physics in a math phd program. I know this is a very broad term and means different things to different people. Some math departments actually have physicists on the faculty and actually are thesis advisers for math phds.

Anyway, I have been studying GR and QM and I would like to study quantum field theory in grad school. Particularly constructive quantum field theory. Looks like I'm frankly **** out of luck. I don't see this happening in grad school. I have been looking very diligently for professors who even list constructive quantum field theory as a research interest and the only person I found was Leonard Gross from Cornell.

Seems like the two founders of the field are Arthur Jaffe and James Glimm. Jaffe is in Harvard's Physics department, and even then, I am not even going to bother applying to Harvard's math department. James Glimm is emeritus at Stony Brook, so I don't think that is going to happen either.

I think John Baez has worked on constructive quantum field theory (big surprise, this guy is a great mathematical physicist).

One of my professors said that I would probably have a difficult time finding a professor who would supervise a thesis related to constructive quantum field theory, unless I go overseas. I have looked on many European math departments, and they really blur the line between math and physics. I have found a few in the Netherlands and some in Germany, among others. However, I don't think I have a good chance of being admitted to European universities and from what I hear, it is difficult for Americans to get funding.

Would CQFT just fall under the general heading of C* algebras?

Any thoughts on this? Should I set my sights on maybe a more tangible phd topic? I know this is still very far away, but I would like to have an idea of what is plausible and what isn't.

OK, thanks a lot guys!

 

[oedipa maas]

In Germany and the Netherlands PhD candidates are hired as employees and are paid a good wage - but MSc candidates aren't. If you are a foreign student working towards an MSc you must pay tuition and cover your living expenses.

Since you've already talked to a professor at your current university about what you would like to do in grad school perhaps you can see if he or she can advise you about prospective supervisors in your area of interest. Are there other professors or graduate students who are familiar with your abilities who would be able to give you more advice?

Trying to figure out what to focus on in graduate school is a difficult thing to do - a BSc does not really provide students with enough background to make a good decision about how to specialize. But that is how the system works in the US.

I would suggest that you not worry so much about finding someone who works on "constructive field theory". Perhaps you can broaden your search and then try to pick out some people whose work you think is interesting - and who are based at schools you feel you might be able to be admitted to.

Perhaps you might also make a post describing your interests and the sorts of approaches towards problems that appeal to you. What other subfields of physics and math have you considered?

 

[George Jones]

Take a look this book

https://www.amazon.com/dp/3540610499/?tag=pfamazon01-20

and this research group

http://unith.desy.de/research/aqft.

 

[Maaneli]

I will be applying for grad school this Winter, but from January 2009-September 2009, I will be done with any course work and will not have any money to commute to my school to continue to do research. So I figured it would be a good opportunity to go further in my mathematics and physics studies.

In graduate school I really want to focus on mathematical physics in a math phd program. I know this is a very broad term and means different things to different people. Some math departments actually have physicists on the faculty and actually are thesis advisers for math phds.

Anyway, I have been studying GR and QM and I would like to study quantum field theory in grad school. Particularly constructive quantum field theory. Looks like I'm frankly **** out of luck. I don't see this happening in grad school. I have been looking very diligently for professors who even list constructive quantum field theory as a research interest and the only person I found was Leonard Gross from Cornell.

Seems like the two founders of the field are Arthur Jaffe and James Glimm. Jaffe is in Harvard's Physics department, and even then, I am not even going to bother applying to Harvard's math department. James Glimm is emeritus at Stony Brook, so I don't think that is going to happen either.

I think John Baez has worked on constructive quantum field theory (big surprise, this guy is a great mathematical physicist).

One of my professors said that I would probably have a difficult time finding a professor who would supervise a thesis related to constructive quantum field theory, unless I go overseas. I have looked on many European math departments, and they really blur the line between math and physics. I have found a few in the Netherlands and some in Germany, among others. However, I don't think I have a good chance of being admitted to European universities and from what I hear, it is difficult for Americans to get funding.

Would CQFT just fall under the general heading of C* algebras?

Any thoughts on this? Should I set my sights on maybe a more tangible phd topic? I know this is still very far away, but I would like to have an idea of what is plausible and what isn't.

OK, thanks a lot guys!

Hey Jason,

There is another possibility for studying AQFT here in the US and at a very prestigious university. At Princeton, there is a philosopher of physics/mathematician named Hans Halvorson, who specializes in mathematical physics and its philosophical implications for physics, and in particular AQFT. In fact, he is arguably the most preeminent expert in this field today. And yet, he is in the philosophy department which means it would be easier for you to get accepted to the program. I also happen to personally know him and he is a very friendly, young, and helpful guy. Here is some of his work:

http://web.princeton.edu/sites/philosph/bios/halvorson.htm

Algebraic Quantum Field Theory
Authors: Hans Halvorson, Michael Mueger
202 pages; to appear in Handbook of the Philosophy of Physics
http://arxiv.org/abs/math-ph/0602036

http://www.nd.edu/~cushpriz/2004 Award.htm

Another possibility is the mathematical physics group of Detlef Duerr at Ludwig Maximilien University in Munich. They specialize in mathematical physics, Bohmian mechanics, and mathematical/physical foundations of QFT:

http://translate.google.com/transla...1&ct=result&prev=/search?q=detlef+duerr&hl=en

http://translate.google.com/transla...1&ct=result&prev=/search?q=detlef+duerr&hl=en

Hope this helps.

 

[JasonJo]

Maaneli! Hey, I should've messaged you first about this before I posted it on PF. As usual, super informative stuff, I plan on emailing the Princeton guy in the next few days. I know you were pretty heavy into the physics/philosophy stuff.

Interestingly enough the guy Hans has an MS in math!