mathematical physics and theoretical physics

[devrimci_kürt]

Theoretical physics is closely related to mathematics....

what is difference mathematical physics and theoretical physics ?

[timo]

I would think the difference is that contrary to popular belief theoretical physics is usually not closely related to mathematics whereas mathematical physics probably is.

[devrimci_kürt]

in short..mathematical physics finds the mathematical rigor required in mathe

matics to be more important than the contact with observations.....

 

is it correct?

[timo]

To answer this question I would need to know more about "mathematical physics" than I currently do. All I currently know about it is that a) The term exists, b) ajb said he is doing it and c) that the terminology in his posts is much more formal and abstract than that of the average theoretical physicist.

The adjective "mathematical" for me is a hint that mathematical physics uses more mathematical rigor.

I wouldn't be surprised if mathematical physics was what non-theoreticians expect theoretical physics to be.

[ajb]

Well, there is no real accepted definition of mathematical physics. It usually means one of two things

 

1) "Doing physics like is is maths". So as Atheist has said, putting some rigour into the calculations and constructions of theoretical physicists. For example, one might want to make path integrals well defined, or find exact solutions to some equations. However, for the most part physics is not mathematics.

 

2) Studying the mathematical structures and there generalisations that arise in theoretical physics. This may well be without any reference to a particular physical system. For example, the mathematical structure behind classical mechanics is symplectic geometry.

 

Personally, what I do is more like 2) than 1). I believe that we can understand more about nature by studying the mathematical structures needed in theoretical physics. What one wants to do is "throw away" any confusion that could arise due to a specific physical system and study what is really important- the mathematical structures behind it.

 

Now it is certainly true that theoretical physics and mathematical physics are not independent and "feed" off each other. It is true that mathematical physics is more like mathematics than "physics". A lot of my "physical motivation" comes from quantum field theory and classical mechanics. For example, I like to attend seminars on theoretical particle physics as well as geometry and algebra. (Though I like geometry more than algebra, in this modern world the two are not so distinct!)

 

 

The tools I regularly use are probably more abstract that what a typical theoretical physicist would use. Most of my "tools" come from differential geometry and modern algebra. Category theory is slowly becoming part of my "armoury".

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c) that the terminology in his posts is much more formal and abstract than that of the average theoretical physicist.

 

I'll take that as a huge compliment! Cheers

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You should also be aware of physical mathematics, which is "doing mathematics like it was physics".

 

There are plenty of things in pure mathematics that can be tackled using physics ideas. String theory has been very good at that. Big results include Donaldson's work on 4-manifolds and Witten's work on knot polynomials. Both come from ideas of quantum field theory.

 

I try to think of mathematics in terms of physics as much as I can, when dealing with geometry it can be more straight forward than more abstract algebra.

Edited January 12, 2009 by ajb