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What Is Mathematic Physics? Not sure if I have a realistic understanding...

  1. Nov 27, 2015 #1
    Not sure what Mathematical Physics is. My assumption is that it combines rigorous mathematic formulation in solving or helping to create a mathematical sound framework for Physics. I think my view on this matter is wrong.

    I really like Mathematics and Physics, I do not really care for Chemistry or Biology. However, I do like some aspects in Chemistry. I had a lot of fun working through Kleppner and Kolenkow on my own, and things like Hamiltonian Mechanics is something I am very interested in the near future, once I learn Analysis and learn to put together a decent mathematical proof. I will thank Real Analysis for this.

    Currently, I am majoring in mathematics and would like to complete a degree with a concentration in Pure Mathematics (Atleast a Masters).

    However, I really like physics. Is mathematical physics, the same as having near equal knowledge in both Math and Physics.

    What career paths are possible for someone who does "Mathematical Physics." I will like to teach someday, but I want to do something else after graduation, for a short time.
  2. jcsd
  3. Nov 28, 2015 #2


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    There is no hard and fast definition of "mathematical physics", or of its allied term "theoretical physics". The best that I can do is tell you how I use these terms.

    For me, a "mathematical physicist" is someone who is interested principally in the mathematics that underlies and is exploited by the mathematical models used in physics. Thus gauge theory in physics is in mathematics the study of fibre bundles and their connections, and Hamiltonian mechanics is the study of symplectic and contact geometries. A mathematical physicist identifies, elucidates, develops and applies the mathematics to physical problems. His principal focus is on the mathematics.

    A "theoretical physicist" for me is a physicist who constructs mathematical models and uses them to calculate what ought to be observed in a a laboratory or in an observatory. His principal focus is not the abstract mathematical structure of his models, but the practical application of them to make predictions and to provide explanations of physical phenomena.

    Many of my colleagues argue that there is no difference between a mathematical physicist and a theoretical physicist.

    I wonder if my colleagues who comment on this forum might care to criticise, enlarge or correct my descriptions above? I would be glad to see what they have to say.
  4. Nov 30, 2015 #3
    Mathematical Physics being an equal measure of Math and Physics: No
    Much depends on the department giving a course in Mathematical Physics . Usually Math Physics in the physics department will be heavily physics based with emphasis on special functions; complex variables; applied mathematics. Usually Math physics from the Math Department is putting physics on a firm mathematical basis in theory. If you get degree in Math Physics it will likely be granted in one department or the other (not both).

    On your resume you may have to put down Math or Physics as a major. Computer screens and Human Resources may not accept your nuanced description of you major as Math and Physics. It is likely the computer or HR screener will say with some irritation: Math or Physics. If the position being sought is in physics, they will not accept applications with math majors and vice-versa. You might get a break and get you resume to someone who will read it in more depth and knowledge, but I wouldn't count on it. Currently, I would say physics is a safer major than math if you seek to get a non-teaching exam, (for example at a government or industrial laboratory)
  5. Nov 30, 2015 #4
    I often have the problem of what mathematical physics refers to, too, because it's like math is the framework of physics. If physics doesn't describe nature based on math, it seems not to be qualified to be called physics. When I was in high school, I found chemistry is too superficial because it often describes nature without giving the foundations underlying the description.

    According to your description, I seem to be characterized as a mathematical physicist to huge proportions, but in some sense I am also characterized as a theoretical physicist. My ex-boss, whose research field is the application aspect of quantum computation and quantum information, also said my interest is mathematical physics after I showed him what I am interested in. However, before he judged that my interest falls into the scope of mathematical physics, I kept considering my interest falls into the scope of theoretical physics, because I didn't know what exactly mathematical physics refers to but I deemed theoretical physics refers to the principles, theorems, and formulations used to explain nature. After he judged my interest belongs to mathematical physics, I often think over if that is really the case by considering what I am really interested in. I reckon I am indeed greatly interested in the math structure underlying physics, but I'm also interested in the prediction and explanation of physical phenomena by math models. I reckon though I am greatly interested in the math applied in physics, I usually don't have much interest in the math which has no application in physics though occasionally there is exception. On the other hand, though I'm interested in the application of math models to the prediction and explanation of physical phenomena, that is only to the level of the application to the theoretical physics, at most thought experiments: I am not so interested in the engineering required to put those physical principles into technology; I am also not so interested in analyzing experimental data.

    I found in my undergraduate school time the subjects interesting me the most were theoretical mechanics and thermodynamics; I like those topics intensively containing analytical contents. Then in my graduate school I chose to take a research topic in General Relativity. Though I kept being greatly interested in all those material I need to learn during the process of the research, I finally felt it's like I was mainly engaged in math, not the physics I formerly considered to be, because General Relativity employs differential geometry, which is very math-oriented. But in retrospect, I found classical mechanics, quantum mechanics, statistical mechanics, classical electrodynamics I had studied, though didn't employ differential geometry, were also filled with math analyses though they were always sprinkled with a little bit of physical interpretations. The difference is that the physical interpretations in General Relativity are harder to be understood in an intuitive way. General Relativity discusses those geometrical quantities used to describe the curvedness of spacetime and formulates physical quantities in terms of those geometrical quantities, and thus gives me the feeling like it's all about math based on my conventional understanding of the discipline categorization. But afterwards I think in the past the physics I learnt was the confined case of physics, the flat space setting in nonrelativistics; General Relativity just generalizes it to the relativistics in curved spacetime. And the spacetime is the venue where physical events take place, so it's justified to give a thorough investigation of it and see what influence the geometry of spacetime gives to the physical events taken place on it. Thus I think geometry should be a subfield of physics. A further rationalization for this is the gauge field theory, which describes an interaction field in terms of a field used to recover the symmetry under a certain group operation and gives Field Theory geometrical color.
    Last edited: Nov 30, 2015
  6. Nov 30, 2015 #5


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    First of all, if I want to get an idea of what a field of study is about, I will troll though the JOURNALS on that subject area. After a while, one can have a very good idea of not only the type of topics involved, but also the active areas of research. Did anyone who doesn't know what "Mathematical Physics" is did that? Did you even browse through the arXiv section of this area?

    Secondly, the IoP, I'm sure, spent time and effort (and money) to produce this lovely document. Did you find and read it? Or is it too pedestrian for you?

  7. Nov 30, 2015 #6
    Not sure why you would take a condescending approach in answering my question. I have looked through a few sources, and the definition of mathematical physics, atleast to me, is ambiguous. If you where going to reply in that manner, why even reply for that matter? It was a legitimate question. Not everyone has access to mentors, professors, parents, advisors, or anyone that has knowledge pertaining to a specific question one may ask.

    Is not the goal of physicsnorum to spread information?
  8. Nov 30, 2015 #7


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    You took that all wrong.

    When I teach a class, I don't just spew the material at the students. I tell them how I think, how I approach the problem, so that they can see where I am coming from. I just don't don't give them fish. I teach them how to fish.

    You never indicated if you did anything in trying to answer your question. You never indicated that you did a search, had already attempted to figure out on your own, etc. So I described to you how *I* would try to find the answer to a question like this, i.e. by looking at the journals related to that area. I mistakenly was hoping that next time you encounter such similar problems, you'd know how to find the answer.

    Obviously, I was wrong!

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