What is modern mathematical physics (Q2714670)

Faddeev, who together with V. Popov contributed a lot to our present understanding of gauge fields and their quantization, looks back and tries to give a short account of what has come to be known as mathematical physics. The term does seem to be well defined. Some claim it is the intersection, some the union of both mathematics and physics. In the author's view, it was and still is identical with theoretical physics with a set of useful and ever increasing set of mathematical tools included. The early monographs by F. Morse and H. Feshbach on the one hand and R. Courant and D. Hilbert on the other illustrate the interpretation used by mathematicians of the last century, namely as a theory of differential equations, variational calculus and functional analysis. But, as Faddeev points out, the problems generated by quantum theory forced physicists to consider spectral theory of operators in Hilbert space and Lie groups and their representations. Gravitation theory forced them to include differential geometry, gauge fields the theory of connections in vector bundles. The author concludes with a review of Yang-Mills theory in which he took part.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00069].