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I was reading about mathematical physics on a university website and they said "an education in theoretical physics is..." appearing to imply mathematical physics is theoretical physics. Is this the case? I want an education in theoretical physics or the closest thing to it. The problem is I live in New Zealand and the universities here don't teach it other than this one potentially.

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    $\begingroup$ The phrase "mathematical physics" can mean a lot of different things depending on who is using the term for which purposes. It could mean what is known as "theoretical physics" to laypeople (which is more precisely referred to as "high energy theory" or "high energy particle theory"). However, "mathematical physics" can often be used a specific subfield of mathematics/physics, which is not really concerned with the same things as a high energy theory. I'd have to see the webpage to judge how they are using the term. $\endgroup$ Apr 7, 2021 at 6:59
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    $\begingroup$ Does this answer your question? Difference between theoretical physics and mathematical physics? $\endgroup$ Apr 7, 2021 at 8:35
  • $\begingroup$ You can study theoretical physics at any university which teaches physics. $\endgroup$ Apr 7, 2021 at 9:47

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Both deal with theory rather than with experiments. The most striking difference is the level of rigour being put in. For example: In theoretical physics you solve differential equations, in mathematical physics you solve them as well, but you also prove that the solution exists and is unique or, if it is not unique, you consider all possible solutions and try to give them physical interpretation.

Theoretical physicists sometimes use mathematical notions which are ill defined, for example, the Gauss integral with purely imaginary exponent. They don't care that much about mathematical rigour (but, obviously, still much more than an experimental physicist would do), use the mathematical tools, if they seem useful intuitively, and deal with new physics. Mathematical physicist would rather deal with the problem of making the Gauß integral with imaginary exponent well defined by considering some suiting limit.

But it's not like mathematical physics are just cleaning up after theoretical physicists, which left some mathematical mess while pushing forward the understanding of physics. While making things rigorous, often new questions emerge, dealing with them might give a better understanding of physics.

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  • $\begingroup$ I think it is not only about rigor with equations: theoretical physics is physics, whereas mathematical physics is a branch of math - it is not about understanding the nature, i.e., formulating the equations, but about solving them. $\endgroup$ Apr 7, 2021 at 10:25
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    $\begingroup$ @Vadim Why would writing equations and ignoring divergences be about understanding nature, while writing equations and understanding how to properly deal with the divergences wouldn't? It's not as simple as that. $\endgroup$ Apr 7, 2021 at 10:55
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Mathematical physics

  • In the most general sense mathematical physics means mathematical methods used in physics (i.e., those parts of mathematics that are actually useful in physics applications). E.g., one may be interested in developing new methods of solving sine-Gordon equation and analyzing its solutions - without actually changing the physical situations where equation arises and its applicability to such situations.
  • As @user1379857 mentioned in the comments, sometimes mathematical physics simply means theoretical physics, as opposed to the experimental physics
  • In some places mathematical physics has more specific meaning - e.g., in Russia the title is common to the books and courses dealing specifically with the second order partial differential equations.

Theoretical physics

  • In the most general sense it is doing physics with equations, rather than in a lab, i.e., as opposed to experimental phsyics. Sometimes computational physics is treated as a separate branch as well.
  • The term may more specifically address to the high energy physics, particle physcis or cosmology, thus excluding the theoretical fields that are considered "more mundane" although not necessarily less complex -such as condensed matter theory, quantum optics, etc.
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