What is mathematical physics?

This is a question that naturally arises as I consider myself to be a mathematical physicist, so I do mathematical physics. But what is mathematical physics?

I don’t think there is any fully agreed on definition of mathematical physics and like any branch of mathematics and physics it evolves and grows. That said, there is roughly two common themes:

  • Doing physics like it is mathematics
  • That is trying to apply mathematical rigour in the constructions and calculations of physics. This is often very hard as physics often requires lots of simplifications and approximations. A lot of physical interpretation and intuition can enter into the work. Physics for the most part is not mathematics and lots of results in theoretical physics lack the rigour required by mathematicians.

  • Studying the mathematical structures required in physics and their generalisations
  • Mathematics is the framework in which one constructs physical theories of nature. As such mathematics, as mathematics is fundamental in developing our understanding of the world around us. This part mathematical physics is about studying the basic structures behind physics, often with little or no direct reference to a specific physical systems. This can lead to natural generalisations of the mathematical structures encountered and give a wider framework to understand physics.

    We see that mathematical physics is often closer to mathematics than physics. I see it as physically motivated mathematics , though this motivation is often very technical.

    Of course this overlaps to some extent with theoretical physics. However, the motivation for theoretical physics is to create and explore physical models, hopefully linking them with reality. Mathematical physics is more concerned with the mathematical structures. Both I think are important and feed of each other a lot. Without development in mathematical physics, theoretical physics would have less mathematical structure and without theoretical physics, mathematical physics would lack inspiration.

    29th North British Mathematical Physics Seminar

    I have been invited to give a talk at the 29th North British Mathematical Physics Seminar (NBMPS) in Edinburgh on the 16th February 2011.

    The NBMPS has been running since 2001 and is a forum for mathematical physicists in North Britain to meet up. They organise four one-day meetings that are held in rotation every year in Durham, Edinburgh, York and Nottingham.

    The 29th meeting is in Edinburgh and I am listed a the first speaker!

    The topic of my talk will be my preprint on Odd Jacobi manifolds and classical BV-gauge systems. This paper is also discussed on my blog here.

    I will place a link to the slides in due course.

    I will also place an update of the event at some later date.


    The talk I felt went well. I had a few questions and comments, but nothing off putting or massively critical.


    Update: The slides for the talk can be found here.