What isMathematical Physics

  1. Is mathematical physics the study of phsics that is focused on the mathematics? If it is, would it give me a disadvantage in the field theoretical physics for choosing mathematical physics instead of mathematics in the future?
     
  2. jcsd
  3. for me mathematical physics is synonymous to theoretical physics.
     
  4. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    Mathematical physics is the use and study of objects such as (Derived/Triangulated) Categories, (Projective) Geometry, ALgebra (Quantum Groups, Hopf Algebras etc) to study physics, usually on the Quantum Level (ie not solid state, engineering stuff, or, as far as I've seen, relativistic stuff). You need to be comfortable with at least the notion of a category and defining objects by commutative diagrams, and not being scared of proper (algebraic) geometry such as sheaves over some curve. However, it really is a shifting definition and next year the emphasis could have changed. Look at the papers of Baez, Dolan, Orlov, Lusztig et al to see how it's practised.
     
  5. HallsofIvy

    HallsofIvy 40,946
    Staff Emeritus
    Science Advisor

    Precisely what "mathematical physics" is varies from one person (in the field) to another. It sounds to me like you are considering majoring in or entering a program in "Mathematical Physics". I would recommend that you ask people in that particular program.
     
  6. According to the bit of paper I was sent from the University, I have a degree in mathematical physics. It just meant I did 50/50 Maths/Physics subjects and didnt do any practical work
     
  7. Mathematical physics is just a word used to describe the study of the more mathematical aspects of physics. It tends to study the same sort of areas as theoretical physics, but there is usually a much greater emphasis on mathematical rigour. It also tends to be practised in math departments rather than physics departments, although there are serveral exceptions to this rule.

    A mathematical physicist is likely to choose problems to work on based on mathematical elegance rather than physical meaning. They tend to work within established theories, often cleaning up the mess made by the lack of rigour in much of theoretical physics. They might also generalize the mathematical formalism beyond what is required to describe the physical world. They are not often concerned with experiments and so are unlikely to work on the phenomenology of a theory. As an example, von Neuman could be considered to be the first mathematical physicist due to his approach to quantum mechanics, work on quantum logic and development of von Neuman algebras.

    On the other hand, theoretical physicists are usually more inclined towards new physical concepts and ideas that go beyond established physical phenomena or theories. They tend to rely on physical intuition a lot more in order to figure out how the world works. Phenomenology is an important part of theoretical physics and most theorists hope that their discoveries will be experimentally verified at some point in the future. For example, Einstein was clearly a theoretical physicist rather than a mathematical physicist.

    Having said that, there is no clear dividing line between mathematical and theoretical physics and you will find people working in both the ways I have described in maths and physics departments. Collaboration between the two groups is common and often very fruitful. Many people who build their careers in these fields have done so by hopping between mathematics and physics departments and there is no real obstacle to doing this. For example, I did physics as an undergrad, mathematics for my PhD and now I am back to a physics department for a postdoc.
     
  8. Slyboy:
    You describe your attitude very good. Now since you wrote about Einstein let me ask you and what the opposite direction of studding about mathematics just from physics? ( the real world)

    Moshek
     
  9. Here are some clues from two journals, one print and one electronic.

    from American Institute of Physics - about American Journal of Mathematical Physics --->
    http://jmp.aip.org/jmp/staff.jsp

    Focus and Coverage

    Journal of Mathematical Physics is published monthly by the American Institute of Physics. Its purpose is the publication of papers in mathematical physics – that is, the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. The mathematics should be written in a manner that is understandable to theoretical physicists. Occasionally, reviews of mathematical subjects relevant to physics and special issues combining papers on a topic of current interest may be published.

    Journal of Mathematical Physics welcomes original research of the highest quality in all active areas of mathematical physics, including the following:

    Classical Mechanics
    Conformal Field Theory
    Dynamical Systems
    Electromagnetic Theory (mathematical aspects)
    Ergodic Theory
    Fluid Mechanics (Navier–Stokes equations, models of turbulence)
    Gauge Field Theory
    General Relativity
    Gravitation Theory (classical and quantum)
    KAM Theory (stability and chaos)
    Kinetic Theory
    Many-Body Theory
    Mathematical Methods in Condensed Matter Physics
    Methods in Mathematical Physics
    Nonlinear Partial Differential Equations in Mathematical Physics
    Percolation Models
    Quantum Chaos
    Quantum Computing
    Quantum Field Theory (algebraic and constructive)
    Quantum Mechanics
    Renormalization
    Scattering Theory (classical and quantum)
    Schrödinger Equation (mathematical properties)
    Semiclassical Analysis
    Spectral Theory
    Statistical Mechanics (equilibrium and nonequilibrium)
    String and Brane Theory
    Symmetries
    Symplectic Dynamics
    Supersymmetry

    from Mathematical Physics Electronic Journal --->
    http://www.ma.utexas.edu/mpej/

    "The research subjects will be primarily on Mathematical Physics; but this should not be interpreted as a limitation, as the editors feel that essentially all subjects of Mathematics and Physics are in principle relevant to Mathematical Physics"

    (some MPEJ editorial board specialties)

    Celestial mechanics
    Cellular automata
    Classical mechanics
    Computer-assisted proofs
    C*-algebras
    Dynamical systems
    Ergodic theory
    Interacting particle systems
    K-theory
    KAM theory
    Mathematical problems in solid state physics
    Noncommutative geometry
    Nonlinear elliptic equations
    Nonlinear differential difference equations
    Nonlinear partial differential equations
    Nonlinear waves
    Perturbation theory for Ordinary Differential Equations
    Quantum field theory
    Quantum mechanics
    Schrodinger operators
    Statistical mechanics
    Stochastic processes

    [EDIT]small correction to first list
     
    Last edited: May 1, 2004
  10. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    C* alg, non-com geometry, and K-theory are the more fashionable of those at the moment (Connes thinks they are the way forward, and who are we to argue?).
     
  11. Matt:

    Do you know how A.connes
    end his lecture at the conference "100 to Hilbert"
    during August 2000 in U.C.L.A university?


    Moshek
     
  12. Moshek,

    I don't understand your question.

     
  13. did he lecture about non commutative geometry in this conference?
    if yes perhaps he showed an example of non commutivaty.
     
  14. Njorl

    Njorl 875
    Science Advisor

    Most grad programs in physics have a set of core course that you need to pass. Usually, these include

    Classical mechanics
    Quantum mechanics
    Statistical mechanics
    Electromagnetic fields
    Math methods (often called math physics, or mathematical methods of theorectical physics etc)

    While you learn a lot of math just getting the basics of the other courses, there are still a lot of things you need to learn. Math methods spans a lot of different subjects of physics and math to round out your set of tools. The one thing that really sticks with me about my math methods course is the calculus of residues. I remember feeling like I learned a magic trick when I learned that. I was so excited I wanted to show my friends. That reminds me. I lost a lot of friends back then.

    Njorl
     
  15. Sorry guys. My computer caught a virus for the past few weeks, so I haven't been able to reply..

    About a week ago, I read an article by an ex-Stanford Physics professor. He mentioned the joke

    What is the difference between mathematical physics and theoretical physics?

    Theoretical physicis are done by physicists who lack the necessary skills to do experiments, and mathematical physics are done by mathematicians who lack the necessary skills to do real mathematics.

    Quite amusing...
     
  16. this joke is a paraphrase of a joke which was given by freedman (he has some solutions of einstein equations) he used with physicists mathematicians and meterologists.
     
  17. So what does Freedman say exactly in his joke?

    Nice discussion! I'll have to choose within a month or so which master I'll start next year.
    I still don't know for sure.. math phys. :uhh: th. phys.
     
  18. "bad mathematicians become physicists, and bad physicists become meterologists."
     
  19. A good mathematician
    can see himself unify with
    the world of phenomena
    as working with the duality
    of symbols
    like in numbers
    ordinals and cardinals

    Very strangely but
    at that point
    there is no more Physics.

    Moshek
     
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?