### Mathematics in Engineering

2021, Issue 6:1-24. doi: 10.3934/mine.2021045
Research article Special Issues

# Foundations of physics in Milan, Padua and Paris. Newtonian trajectories from celestial mechanics to atomic physics

• Received: 06 March 2020 Accepted: 28 August 2020 Published: 09 November 2020
• This paper is written, in a very informal and colloquial style, on the occasion of the seventieth birthday of Antonio Giorgilli. The aim is to describe how his first scientific works were actually conceived within a group that happened to be formed in the years seventies with an ambitious program on the foundations of physics. Namely, to understand whether the recent (at those times) progress in dynamical systems theory might allow one to enlighten in some new way the relations between quantum mechanics and classical physics. This required to understand what impact dynamical systems theory may have on the foundations of classical statistical mechanics (with particular attention to the Fermi-Pasta-Ulam problem), and on matter-radiation interaction. In such a frame Celestial Mechanics too started to be addressed, particularly by Antonio, initially just as a kind of a byproduct. Here a recollection is given of how the group was formed. Then a quick review is given of the results obtained, the attention being mainly addressed to those relevant for the original foundational program.

Citation: L. Galgani. Foundations of physics in Milan, Padua and Paris. Newtonian trajectories from celestial mechanics to atomic physics[J]. Mathematics in Engineering, 2021, 3(6): 1-24. doi: 10.3934/mine.2021045

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• This paper is written, in a very informal and colloquial style, on the occasion of the seventieth birthday of Antonio Giorgilli. The aim is to describe how his first scientific works were actually conceived within a group that happened to be formed in the years seventies with an ambitious program on the foundations of physics. Namely, to understand whether the recent (at those times) progress in dynamical systems theory might allow one to enlighten in some new way the relations between quantum mechanics and classical physics. This required to understand what impact dynamical systems theory may have on the foundations of classical statistical mechanics (with particular attention to the Fermi-Pasta-Ulam problem), and on matter-radiation interaction. In such a frame Celestial Mechanics too started to be addressed, particularly by Antonio, initially just as a kind of a byproduct. Here a recollection is given of how the group was formed. Then a quick review is given of the results obtained, the attention being mainly addressed to those relevant for the original foundational program.

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