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Richard Feynman et la mécanique quantique : genèse, développement et pérennité du concept d'intégrale de chemins

Abstract : After the upheavel, both intellectual and philosophical, which the quantum and special relativity theories stirred, the twentieth century was marked by the need to understand the true nature of fundamental interactions.The contribution of the physician Richard Feynman (11 May 1918 - 15 February 1988) in the knowledge of theses interactions concems our work, because through an audacious mathematical formulation, he found method of path integrales.Feynman's work through genesis, development and longevity of path integral are the subject of my thesis. The thesis is divided into nine chapters:The first one takes place on the hand between 1900 and 1941 regarding Quantum mechanics histoy part. We also find the description of a complete panorama (1927 à 1941) about problems of this new science conceming coupling between elctromagnetic fields and electric charges at quantum level.The second chapter covers the period between 1939 and 1949 when Feynman was studying at Massachusetts Institut of technology. This chapter begins by introducing Feynman in order to grasp the way his father fashioned his perception of natural things so as to understand the man's nature, his thougt and his originality. Lastly, we devote a tapie to Feynman's point of view on Quantum Theory so as to find out what initially motived him and what issue he wanted solved.The third chapter takes place between 1939 and 1941 when Feynman was studying at Princeton in order to obtain his Philosophiae doctor (PhD). We detail the history of the different stages of Feynman's research work which will gradually orient him towards the discovery of the path integral. lt ends with the way in which Feynman finds (in 1941) the Schrôdinger equation.The fourth chapter contains the thoughts and work of Feynman conceming the construction of the action that will be subject of his doctoral thesis will be presented in June 1942. lt shows how the future theoretical physicist connects the wave function to the Lagrangian in order to see quite naturally the notion of path for a particle in space-time .The fifth chapter takes place on the hand between 1942 and 1948. This is a period during which the young American physicist deeply reflects on an idea of multiple trajectories of a particle in space-time, i.e. on the construction of an integral including as variable of integration ail the paths of a region of space-time, in order to build a new formalism in quantum mechanics.The sixth chapter, based on the two publications dating September 1949, shows the solution implemented by Feynman to vizualise path integral in term of drawings, as well as his method of calculation .ln the seventh chapter, we examine the mathematical works on path integrales (from 1951 to 2020). oriented towards the research of a rigourous foundation of these integrals, according to different approach.The eighth and ninth chapters concem concem the longevity of the path integrales concept through Fields Quantum Theory and through fundamental mathematics that could benefrt a better understanding about theorems and original structures allowing a generalization faciliting connections between their different branches; even extrapoling new points of view.
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Alain Bousselin. Richard Feynman et la mécanique quantique : genèse, développement et pérennité du concept d'intégrale de chemins. Histoire, Philosophie et Sociologie des sciences. Université de Pau et des Pays de l'Adour, 2021. Français. ⟨NNT : 2021PAUU1090⟩. ⟨tel-03252449⟩

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