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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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | From Point Particles to Gauge Field Theories: a Differential-Geometrical approach to the Structures of the Space of Solutions |
| Autori: | Autore Email Schiavone, Luca luca.schiavone@unina.it |
| Data: | 13 Dicembre 2022 |
| Numero di pagine: | 170 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | 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 |
| Data: | 13 Dicembre 2022 |
| Numero di pagine: | 170 |
| Parole chiave: | multi-symplectic geometry, pre-symplectic geometry, space of solutions |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
| Depositato il: | 03 Gen 2023 10:20 |
| Ultima modifica: | 09 Apr 2025 14:16 |
| URI: | http://www.fedoa.unina.it/id/eprint/14653 |
Abstract
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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