Types of quantum field thories
Mathematical physics is a discipline at the interface of mathematics and physics, concerned with developing mathematical models of physical phenomena and mathematical apparatus arising or needed in such models. It intersects with theoretical physics which deals with theoretical arguments in consideration of physical phenomena and the development of models of known and of conjectured physics; theoretical physics is in a sense wider as it deals also with interpretations, non-rigorous and sometimes speculative argument from experiments or from rough comparisons of different models and various experimental data, not entering or forming together a necessarily compatible mathematical entity. For example, the calculations of fitting parameters and adjusting models to complicated experimental data, called the phenomenology is part of the work of a theoretical physicist, but most such work is not nowadays considered to belong to mathematical physics, unless one is developing a really new mathematical model or tool for such work.
6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
More recently, one also sometimes uses a less familiar term physical mathematics for the study of mathematical constructions inspired by models of theoretical physics; thus the final aim may be more mathematical (say finding a new topological invariant using physical intuition) than in the mathematical physics. However there is no clean boundary and to some extent the two notions are interchangeable.
See the related, but disputable notion of applied mathematics.
A historically inclined article on mathematical physics is featured on wikipedia.
For an extensive list of literature see
Further related entries include