Mathematical physics
The mathematical physics attempts to the widest possible fields of physics in a mathematical form and analyze with mathematical methods.
The approach is to expose the mathematical structure in the theoretical concepts and calculation methods of physics and conceptually develop. Here mathematics and physics fertilize each other in terms of knowledge.
Demarcation
The mathematical physics deals with the strict mathematical treatment of models of physical phenomena. The transitions to theoretical physics, where the requirements of mathematical rigor are usually kept somewhat weaker, there are fluid.
Important problems of mathematical physics are:
- Schrödinger operators in Hilbert spaces - for example for the evolution of systems of quantum mechanics and spectral theory
- Exact solutions of Einstein's field equations of general relativity
- Exact solutions of systems of statistical mechanics and random matrices
- Symplectic geometry as an overarching mathematical structure of classical mechanics, quantum mechanics and other areas of physics
- Many questions of string theory such as dualities and the holographic principle
To be distinguished from the actual mathematical physics are the courses and courses for Mathematical Methods in Physics, which are the physicists teach the necessary mathematical basic knowledge offered at many universities. The focus is on a possible wide and application-specific, tailored to the needs of the physics representation of mathematical methods and less on techniques of proof or proofs of mathematical theorems as in pure mathematics lectures. Major areas of focus are the topics vector spaces and vector algebra, simple tensor ( linear algebra ), vector analysis and potential theory, function theory ( residue theorem ), special functions ( spherical functions, Legendre polynomials, etc.), ordinary and partial differential equations, Fourier analysis and probability theory, including stochastic processes.
Some areas of research and Associations
The international organization of mathematical physics is the International Association of Mathematical Physics ( IAMP ), which organizes international congresses every three years.
In Germany is dedicated to the Max Planck Institute for Mathematics in the Sciences in Leipzig some aspects of mathematical physics. In Vienna there is the Erwin Schrödinger Institute for Mathematical Physics at the initiative of Walter Thirring, of a strong school of mathematical physics built in Vienna. In Paris, the Institut Henri Poincaré has traditionally been a focus in mathematical physics.
The German DMV Section "Mathematical Physics" calls it a goal to be open to all mathematicians / inside, who are interested in the mathematical treatment of physically motivated problems. It promotes the contact between the mathematical physicists in Germany (meetings, technical literature, mailing list).
Analog math specialist groups there are in other countries, and also in the context of physics. The cooperation DMV - German Physical Society is to be deepened in order not to fall into competition of the two subject areas.
Especially for achievements in mathematical physics of the Dannie Heineman Prize and the Henri Poincaré Prize of the IAMP will be awarded.