Euler, Riemann, Ramunijan, Feynman, Dyson, Schwinger…and Operational calculus

Auditorium B. Touschek (Laboratori Nazionali di Frascati, Via Enrico Fermi 40, Frascati)

Auditorium B. Touschek

Laboratori Nazionali di Frascati, Via Enrico Fermi 40, Frascati

Via Enrico Fermi 40 00044 Frascati

Particular families of special functions, conceived as purely mathematical devices between the end of XVIII and the beginning of XIX centuries, have played a crucial role in the development of many aspects of modern Physics. This is indeed the case of the Euler gamma function which has been one of the key elements paving the way to string theories, furthermore the Riemann Zeta function has played a decisive role in the development of renormalization theory. The ideas of Euler, Riemann, Ramunijan and of other, less popular, mathematicians have therefore provided the mathematical apparatus ideally suited to explore, and eventually solve, problems of fundamental importance in modern Physics. The theory of renormalization traces back to the work on divergent series by the mathematicians of two centuries ago. Feynman, Dyson, Schwinger… rediscovered most of these mathematical “curiosities” and were able to develop a new and powerful way of looking at physical phenomena. The Feynnman operational calculus, of fundamental importance to deal with the operator algebra and/or with the computation of integrals in QED, ad already been developed by the operationalists well before the invention of quantum mechanics itself. In this seminar we discuss the close link between Mathematics and Physics and also comment on the possibility that Physics may contribute to the solution of “hot” mathematical problems as the Riemann hypothesis.

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