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The last decade witnessed an increasing interest of mathematicians
in prob lems originated in mathematical physics. As a result of
this effort, the scope of traditional mathematical physics changed
considerably. New problems es pecially those connected with quantum
physics make use of new ideas and methods. Together with classical
and functional analysis, methods from dif ferential geometry and
Lie algebras, the theory of group representation, and even topology
and algebraic geometry became efficient tools of mathematical
physics. On the other hand, the problems tackled in mathematical
physics helped to formulate new, purely mathematical, theorems.
This important development must obviously influence the
contemporary mathematical literature, especially the review
articles and monographs. A considerable number of books and
articles appeared, reflecting to some extend this trend. In our
view, however, an adequate language and appropriate methodology has
not been developed yet. Nowadays, the current literature includes
either mathematical monographs occasionally using physical terms,
or books on theoretical physics focused on the mathematical
apparatus. We hold the opinion that the traditional mathematical
language of lem mas and theorems is not appropriate for the
contemporary writing on mathe matical physics. In such literature,
in contrast to the standard approaches of theoretical physics, the
mathematical ideology must be utmost emphasized and the reference
to physical ideas must be supported by appropriate mathe matical
statements. Of special importance are the results and methods that
have been developed in this way for the first time."
The last decade witnessed an increasing interest of mathematicians
in prob lems originated in mathematical physics. As a result of
this effort, the scope of traditional mathematical physics changed
considerably. New problems es pecially those connected with quantum
physics make use of new ideas and methods. Together with classical
and functional analysis, methods from dif ferential geometry and
Lie algebras, the theory of group representation, and even topology
and algebraic geometry became efficient tools of mathematical
physics. On the other hand, the problems tackled in mathematical
physics helped to formulate new, purely mathematical, theorems.
This important development must obviously influence the
contemporary mathematical literature, especially the review
articles and monographs. A considerable number of books and
articles appeared, reflecting to some extend this trend. In our
view, however, an adequate language and appropriate methodology has
not been developed yet. Nowadays, the current literature includes
either mathematical monographs occasionally using physical terms,
or books on theoretical physics focused on the mathematical
apparatus. We hold the opinion that the traditional mathematical
language of lem mas and theorems is not appropriate for the
contemporary writing on mathe matical physics. In such literature,
in contrast to the standard approaches of theoretical physics, the
mathematical ideology must be utmost emphasized and the reference
to physical ideas must be supported by appropriate mathe matical
statements. Of special importance are the results and methods that
have been developed in this way for the first time."
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