Escalante Hernández, AlbertoESCALANTE HERNANDEZ, ALBERTO; 122254Zavala Pérez, Víctor Alberto2024-11-152024-11-152024-01-22https://hdl.handle.net/20.500.12371/22394"This dissertation conducts an in-depth analysis of two higher order systems: the extended Maxwell-Chern-Simons theory and Weyl gravity. Higher-order theories, identifiable by the inclusion of time derivatives of third order or higher in the Lagrangian, exhibit interesting properties. On one hand, these theories demonstrate distinct dynamics, enabling them to fit experimental data and serve as viable models in situations where traditional theories deviate from empirical observations. On the other hand, challenges such as the Ostrogradsky instability and the loss of unitarity are prevalent in these theories. Due to their intricacy, the “Hamiltonization” procedure is highly non-trivial, necessitating the incorporation of sophisticated mechanisms. This study makes use of the Faddeev-Jackiw and Hamilton-Jacobi Hamiltonization methods, introducing additional degrees of freedom as an order reduction mechanism and obtaining a first-order Hamiltonian with equivalent dynamics. This process introduces constraints among variables, which must be properly treated for the dynamics to remain consistent. These frameworks are used to find the canonical structure of the actions, the symmetries of both theories and establish the algebra of the constraints".pdfengCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRAAstronomía-- Geodesia-- Determinaciones de la gravedadFísica-- Constitución y propiedades de la materia-- Ondas gravitacionalesFísica-- Constitución y propiedades de la materia-- Física de la relatividadFísica-- Constitución y propiedades de la materia-- Mecánica cuánticaAstronomía-- CosmologíaTesis de doctoradoopenAccess