Mathematical physics

Mathematical physics is a scientific discipline aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. Mathematical physics covers a very broad area of topics with the common feature that they blend pure mathematics and physics. Although mathematical physics and theoretical physics are related, these two notions are often distinguished 1. Mathematical physics emphasizes the mathematical rigor of the same type as found in mathematics while theoretical physics emphasizes the links to 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. Some compensation for the fact that mathematicians tend to call mathematical physicists physicists and that physicists tend to call them mathematicians is provided by the breadth of physical subject matter and beauty of various unexpected interconnections in the mathematical structure of rather distinct physical situations.

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.
• A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton, 2004. ISBN 1-58488-355-3
• A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2002. ISBN 1-58488-299-9