From point particles to gauge field theories: a differential-geometrical approach to the structures of the space of solutions

Autores: Luca Schiavone
Directores de la Tesis: Luis Alberto Ibort Latre (dir. tes.)
Lectura: En la Universidad Carlos III de Madrid ( España ) en 2023
Idioma: inglés
Tribunal Calificador de la Tesis: Eva Miranda Galcerán (presid.) , Maria Carmela Lombardo (secret.) , Alberto Calabri (voc.) , Fernando Falceto Blecua (voc.) , Katarzyna Grabowska (voc.) , María Edith Padrón Fernández (voc.) , Narciso Román Roy (voc.) , Marco Castrillón López (voc.)
Enlaces
- Tesis en acceso abierto en: e-Archivo
Resumen
- 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.