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.)
• Programa de doctorado: Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid
• Materias:
  • Matemáticas
    • Investigación operativa
      • Sistemas de control
  • Física
    • Física teórica
      • Campos
• 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.