Cuantizaciónn de la teoría de Horava en 2+1 dimensiones
The main objective of the doctoral research is to address the quantization of the complete non-projectable Horava theory in 2+1 dimensions. Within the quantization program we propose the Hamiltonian formalism and we study the consistency of the link algebra. The definition of asymptotic flatness of...
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| Tipo de documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2021 |
| País: | Chile |
| OAI Identifier: | oai:repositorio.anid.cl:10533/42581 |
| Acesso em linha: | https://hdl.handle.net/10533/42581 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Ciencias Naturales Ciencias Físicas Otras Especialidades de la Física |
| Resumo: | The main objective of the doctoral research is to address the quantization of the complete non-projectable Horava theory in 2+1 dimensions. Within the quantization program we propose the Hamiltonian formalism and we study the consistency of the link algebra. The definition of asymptotic flatness of the non-projectable theory in 2+1 dimensions is established and the gravitational energy necessary for the Hamiltonian to be differentiable is found. All this motivated by the exact solution found when solving the case of a particle at rest coupled to the Horava action, which geometrically represents a cone with an angle of deficit or excess with a singularity at the origin and whose interior is flat. We propose the quantization of the theory via the functional integral, which requires calculating the appropriate measure for the first and second class bonds. We study the physical consequences of this measure in the dynamics of the theory, where second-class links play a fundamental role in the regularization of the propagator of the span function. Due to an ordering criterion in perturbations, some propagators associated with the non-gauge part are not regular, regardless of the canonical gauge condition chosen. In order to include more general gauge fixation conditions, for example, the gauge fixation condition is not local and non-canonical, with which the consistent quantization and renormalization of the projectable Horava theory was demonstrated. The BFV (Batalin-Fradkin-Vilkovisky) quantization study was performed. The theory possesses a BRST symmetry, with its help it is shown that the gauge-fixed quantum Hamiltonian is invariant under this residual symmetry, furthermore, the functional integral is independent of the chosen gauge condition and is independent of non-physical degrees of freedom. Therefore, the BFV theory has a unitary matrix S. The method is to extend the phase space, promoting the Lagrange multipliers associated with the first-class links to canonical variables with their respective conjugate moments, and adding a couple of ghosts with opposite stat to the first class bonds. We show in this investigation that Horava's theory not projectable in 2+1 dimensions is rank one according to the BFV definition. Consequently, we find the generator of the BRST symmetry, which leaves the Horava action invariant in the extended space, where the bonds are resolved. Furthermore, with the help of the BRST generator, it is shown that the path integral of the Horava theory in extended space is independent of the gauge fixation condition. Unlike path integral quantization, BFV phantoms take on a term kinetic, on the contrary, the ghosts associated with the second-class bonds remain non-regular due to the second-order criterion in perturbations. We also present studies on the Hamiltonian formulation at the critical point λ=1/d, where λ is the constant coupling of the kinetic term and d is the spatial dimension. For this value of the critical point, the kinetic term is invariant under anisotropic Weyl scaling. One consequence of this value is that the physical scalar mode is deleted. We propose the canonical formulation of the anisotropic conformal theory, which is invariant under anisotropic Weyl scaling in 3+1 dimensions. We make the dynamic comparison between two conformal potentials, the Cotton square conformal potential and a conformal potential proposed in this research that depends on the metric and the span function, this has conformal weight -3 and degree of anisotropy z=3, minimum order for renormalization by counting powers. Furthermore, we compare the dynamics of this completely conformal theory with the conformal kinetic theory (where only the kinetic term is Weyl invariant). The kinetic-conformal theory was investigated in 2+1 dimensions, the canonical formulation was established from which it follows that the theory does not have degrees of freedom, just like general relativity. We find for certain conditions in the parameter space, asymptotically flat vacuum solutions are globally flat. Also, relaxing the boundary conditions non-planar solutions were found, unlike general relativity that all its vacuum solutions are flat in 2+1 dimensions. We have made contributions that approach the consistent quantization of the non-projectable version of Horava, we hope that these steps will serve as a starting point to deepen the knowledge of the theory and perhaps to prove its renormalization. |
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