Desarrollo de los formalismos de Gitman-Lyakhovich-Tyutin y Hamilton-Jacobi aplicados a sistemas gravitacionales de alto orden: Gravedad de Weyl
Date
2024-01-22
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Benemérita Universidad Autónoma de Puebla
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"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".
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