Which kind of mathematics for Quantum Mechanics?
The relevance of H. Weyl's a program of research.
Antonino Drago
Dept. of Physical Sciences, Univ. "Federico II", Naples
In 1918 Weyl's book Das Kontinuum planned to found anew mathematics upon more conservative bases than both rigorous mathematics and set theory. It gave birth to socalled Weyl's elementary mathematics, i.e. an intermediate mathematics between the mathematics rejecting at all actual infinity and the classical one including it almost freely.
Abstract
In 1918 Weyl's book Das Kontinuum planned to found anew mathematics upon more conservative bases than both rigorous mathematics and set theory. It gave birth to socalled Weyl's elementary mathematics, i.e. an intermediate mathematics between the mathematics rejecting at all actual infinity and the classical one including it almost freely.
The present paper scrutinises the subsequent Weyl's book Gruppentheorie und Quantenmechanik (1928) as a program for at the same time founding anew theoretical physics  through quantum theory  and developing his mathematics  through the improvement of group theory  a mathematical theory effacing  according to Weyl  the old distinction between discrete and continuous mathematics. Evidence from Weyl's writings is collected for supporting this interpretation.
Then Weyl's program is evaluated as unsuccessful, owing to some crucial difficulties of both physical and mathematical nature.The present clearcut knowledge of Weyl elementary mathematics allows us to reevaluate Weyl's program in order to look for more adequate formulations of quantum mechanics in this kind of mathematics as well as in any weaker kind of mathematics than classical one.
Info
Drago A.: Which kind of Mathematics for quantum mechanics? The relevance of H. Weyl's program of research, in A Garola & A Rossi (eds.): Proceedings Foundations of Quantum Mechanics. Historical Analysis and Open Questions World Scientific, Singapore, 2000, pp. 167193
