What do mathematical physicists work on?

[Nano-Passion]

How do they differ from theoretical physicists? I was looking into arXiv papers in the mathematical physics portion and saw things like the physics of hoolahoops..I hope no offense is taken but I thought that was bit funny haha. On a more serious note, how are theoretical and mathematical physics different? It seems like the same thing but different terms.

 

[homeomorphic]

Mathematical physics is a pretty generic and broad term.

I would tend to consider someone who does things more rigorously and uses more heavy math tools to be a mathematical physicist. Definitely different from theoretical physics, I would say.

When I think of mathematical physics, I think of quantum gravity, some topics in quantum computing, and maybe some more PDE-oriented stuff.

The term is kind of self-explanatory, if you understand the difference between math and physics.

 

[I like Serena]

I think you may call Murray Gell-Mann a mathematical physicist.
He came up with the quark model based on abstract mathematical group theory.
That gave some resistance in the physics community, which was broken because nothing fitted better.

 

[Nano-Passion]

Mathematical physics is a pretty generic and broad term.

I would tend to consider someone who does things more rigorously and uses more heavy math tools to be a mathematical physicist. Definitely different from theoretical physics, I would say.

When I think of mathematical physics, I think of quantum gravity, some topics in quantum computing, and maybe some more PDE-oriented stuff.

The term is kind of self-explanatory, if you understand the difference between math and physics.

But theoretical physicists work on string theory and quantum gravity?

I think you may call Murray Gell-Mann a mathematical physicist.
He came up with the quark model based on abstract mathematical group theory.
That gave some resistance in the physics community, which was broken because nothing fitted better.

I'm surprised I haven't heard of him before (or maybe just don't recall); he had a lot of important contributions.

 

[Sina]

Theoretical physicists use mathematics as a tool to solve problems in physics or formulate theories etc. Mathematical physicists try to understand physical systems, theories or problems by their interaction with mathematics. In this case mathematics is a separate world, having its own rules, structure etc. This world in certain ways restricts and interacts with the physical world which can be used to understand it.

For instance I would think that the study of the mathematical properties of symmetries to impose rules on physical systems is more like mathematical physics. Once you know that the system obeys certain symmetries, then the mathematical structure of those symmetries can be used to gather more information about the system. However if you use symmetries (and the knowledge available on them) to calculate some properties of the system that would be more like theoretical physics. Another example would be studying infinite dimensional geometry or non-commutative geometry to understand the structure of quantization through geometric structure and then in some way define a geometric passage from quantum to classical world would be mathematical physics. Using idea of quantization to quantize EM field would be theoretical physics.

etc etc

One general rule would be, if you take a physical system and somehow transform into a purely mathematical system and study its properties in the mathematical world and then transform the results back to the physical world then that would be mathematical physics. This definition is not sufficient however since even at the first step, the physical systems is usually again described by some axioms derived from experiment and the rest is again mathematics. So term mathematical physics is more geared towards "modern mathematical topics". Or simply solving the Newton's equation should then be considered mathematical physics since you are using the restrictions imposed by the theory of ODE to explore properties of the system :)

I guess we could refine the above idea by saying "if %80 of the non-experimental pure physicists know the mathematics you are using then it is theoretical physics" heh

 

[homeomorphic]

But theoretical physicists work on string theory and quantum gravity?

It's not the topic. It's the style. Mathematical physicists do the same topics, but their style is more mathematical or they study the more mathematical aspects of those subjects.

 

[SophusLies]

Mathematical physicists can back up their math with proofs and rigorousness. While many theoretical physicists can use high level math very well, most don't care or have time to do proofs. I took two classes with an actual "mathematical physicist." He had incredible control of math, especially with proofs. He knew physics intimately too but he didn't care how well the theory meshed with experiments, which is the most important goal for a theoretical physicist, he mostly cared

A main difference is a mathematical physicist resides in the math department while a theoretical physicist is in the physics department.

 

[Nano-Passion]

Thanks to everyone here for their replies and patience.

 

[dextercioby]

There's no absolute boundary among the 2 disciplines. Not to me, at least. However, one can spot differences. A theoretical physicist creates physics using mathematics, just like Einstein did with GR or Pauli did with PCT and spin-statistics, a true mathematical physicist would love to write a physics book (for ex. a quantum mechanics book) with the following pattern: definitions, axioms, lemmas, theorems, appendix: glossary of mathematical terms, appendix: guide to bibliography, bibliography of at least 400 items including physical interpretation of the axioms + theorems.

In terms of pointwise examples, for me the PhD thesis of Rafael de la Madrid is a mathematical physics primer, just like the QFT text by BLT 1975, while the book of Griffiths on Quantum mechanics is theoretical physics; likewise 10 volumes of L&L. The famous 3 set of Weinberg captures elements of both. Et caetera .

 

[EternityMech]

where I am from Mathematical Physics is a subbranch of Theoretical Physics. and they work in the physics department.

 

[homeomorphic]

A main difference is a mathematical physicist resides in the math department while a theoretical physicist is in the physics department.

That's a good rule of thumb, but not strictly true.