Higher-order time derivative theories. Interpretation, instability and possible stabilization

Higher-derivative field theories are well known to propagate ghost degrees of freedom (DOFs), an instability known as of Ostrogradsky. However, recent advances proposing conditions to stabilize this kind of models, with finitely many unstable DOFs in a non-minimal way, by including a stabilizer DOF and a kinetic coupling between both, have opened the question whether an extension of this methodology to relativistic field theories, also works. In this thesis, the Pais-Uhlenbeck Lagrangian density with a higher derivative scalar field, which leads to an unstable theory, is considered as a basis for a toy model. Upon the requirement for the Lagrangian to be a Lorentz scalar, as well as for the transformation properties of both, the unstable and the stabilizer DOF, to be consistent with a kinetic constraint that controls the instability, it is first concluded that at the level of a free theory the stabilizer must be a vector field. The latter is also motivated to make plausible an extension to interacting higher derivative theories. This is, the kinetic instability should be controled already at the free theory, in such a way that the Feynman propagator does not show a ghost DOF. A Hamiltonization with constraints is considered in order to deal with the imposed kinetic- constraint, which is at the core of the stabilization. This approach allows to examine the properties of the Ostrogradskian instability as it has been done up until now in the literature, therefore making evident the successful extension of the stabilization properties, at least in this toy model. Furthermore, the physical DOFs propagated by the theory are found, and the physical Hamiltonian written in terms of these, turns out to be positive definite and bounded from below in certain region of parameter space. In particular, a very interesting relation between the coupling parameter (α) of the higher-derivative term of the scalar field and the mass of the stabilizer field (m), arises as a requirement for the stabilization. The condition is a lower bound on the former, of the form α 1/m. Such relation was completely unexpected but more meaningful for the physical interpretation of the new higher-derivative structure, because it would show the energy scale at which these new terms may become important.

• Autores: Valencia Villegas, Juan Mauricio
• Fecha de publicación: 2017
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/63363
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/63363; http://bdigital.unal.edu.co/63666/
• Palabra clave: 5 Ciencias naturales y matemáticas / Science; 53 Física / Physics; Higher derivatives; Ostrogradskian instability; Quantum theories; Quantization with constraints; Derivadas altas; Inestabilidad de Ostrogradsky; Teorías cuánticas; Cuantización con ligaduras
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional