Mathematical physics is an interdisciplinary field of academic study in between mathematics and physics, aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. Although mathematical physics and theoretical physics are related, these two notions are often distinguished. Mathematical physics emphasizes the mathematical rigor of the same type as found in mathematics while theoretical physics emphasizes the links to actual observations and experimental physics which often requires the theoretical physicists to use heuristic, intuitive, and approximate arguments. Arguably, mathematical physics is closer to mathematics, and theoretical physics is closer to physics.
Because of the required rigor, mathematical physicists often deal with questions that theoretical physicists have considered to be solved for decades. However, the mathematical physicists can sometimes (but neither commonly nor easily) show that the previous solution was incorrect.
Quantum mechanics cannot be understood without a good knowledge of mathematics. It is not surprising, then, that its developed version under the name of quantum field theory is one of the most abstract, mathematically-based areas of physical sciences, being backward-influential to mathematics. Other subjects researched by mathematical physicists include operator algebras, geometric algebra, noncommutative geometry, string theory, group theory, statistical mechanics, random fields etc.
Bibliographical references
- P. Szekeres, A Course in Modern Mathematical Physics: Groups, Hilbert Space and differential geometry. Cambridge University Press, 2004.
- J. von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton University Press, 1996.
- J. Baez, Gauge Fields, Knots, and Gravity. World Scientific, 1994.
- R. Geroch, Mathematical Physics. University of Chicago Press, 1985.
- R. Haag, Local Quantum Physics: Fields, Particles, Algebras. Springer-Verlag, 1996.
- J. Glimm & A. Jaffe, Quantum Physics: A Functional Integral Point of View. Springer-Verlag, 1987.
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Important publications in Mathematical physics
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