Schiavone, Luca (2022) From Point Particles to Gauge Field Theories: a Differential-Geometrical approach to the Structures of the Space of Solutions. [Tesi di dottorato]
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| Item Type: | Tesi di dottorato |
|---|---|
| Resource language: | English |
| Title: | From Point Particles to Gauge Field Theories: a Differential-Geometrical approach to the Structures of the Space of Solutions |
| Creators: | Creators Email Schiavone, Luca luca.schiavone@unina.it |
| Date: | 13 December 2022 |
| Number of Pages: | 170 |
| Institution: | Università degli Studi di Napoli Federico II |
| Department: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 35 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gioconda.moscariello@unina.it |
| Date: | 13 December 2022 |
| Number of Pages: | 170 |
| Keywords: | multi-symplectic geometry, pre-symplectic geometry, space of solutions |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
| Date Deposited: | 03 Jan 2023 10:20 |
| Last Modified: | 09 Apr 2025 14:16 |
| URI: | http://www.fedoa.unina.it/id/eprint/14653 |
Collection description
We study the geometry of the space of solutions of the equations of motion of (a large class of) classical field theories. In particular, we exhibit the existence of a canonical pre-symplectic structure on it and we argue whether and how it is possible to use it to define a Poisson structure. Within gauge theories we show how a construction related to the so-called coisotropic embedding theorem can be suitably used to this scope. Several concrete physical systems are considered, such as the free particle as an example of mechanical system and Klein-Gordon theory, free Electrodynamics, Yang-Mills theories and Palatini's Gravity as examples of field theories.
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