A carregar...
Publicação
The BFCG theory and canonical quantization of gravity
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 880.77 KB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
Of the four interactions known in Nature, gravity is the most accessible to the senses. The best description we have, so far, of the gravitational interaction is the theory of General Relativity (GR) developed by Albert Einstein in the beginning of the XXth century. This same century also witnessed the birth of Quantum Theory. This means that the Principle of Uncertainty formulated by Werner Heisenberg must be taken into account in the construction of physical theories. This way a programme was set up to quantize interactions. This quantization was accomplished in all but the gravitational force. GR in fact is a classical theory. The most commonly used method to carry forth the quantization of a theory is called Canonical Quantization (CQ). This method applied to GR gives rise to the Wheeler–DeWitt equation which is ill defined and notoriously hard to solve. This difficulty is for the most part connected to the non-polynomial character of the Hamiltonian Constraint (HC). To alleviate this problem, Abhay Ashtekar found a new set of variables for GR. Written in these variables, the HC has a polynomial character. However, given that Ashtekar’s variables are complex, the necessity arises for a new condition, the reality condition which is very hard to quantize. A real version of Ashtekar’s variables may be used but the Hamiltonian Constraint is again non-polynomial. The difficulties of solving the HC in the canonical formalism have led to the development of a path-integral quantization approach known as spin-foam models (SF). SF models have the problem of the classical limit and the problem of the coupling of fermionic matter. These problems are related to the fact that the edge-lengths, or the tetrads, are not always defined in a SF model of quantum gravity. In order to introduce the edge lengths in the SF formalism, one has to introduce the tetrads in the BF (the letters represent the fields featuring in the action) theory formulation of GR. This can be done by using a formulation of GR based on the Poincaré 2-group. The idea is to reformulate GR as a constrained topological theory of the BFCG (the letters represent the fields featuring in the action) type. This approach is a categorical generalization of the constrained BF theory formulation of GR which is used for the SF models. The BFCG reformulation of GR is useful for the path-integral quantization. In this case one obtains the spin-cube models, which represent a categorical generalization of the SF models. As far as the CQ is concerned, the progress has been hindered because the constrained BFCG theory has a complicated canonical structure. A reasonable strategy is to study first a simpler theory, which is the unconstrained BFCG theory. This is a topological gravity theory, and we will show that its canonical formulation is simple to understand. Another feature of this theory is that it is equivalent to the Poincaré group BF theory, so that one can perform a CQ in terms of the BF theory variables. This is mathematically simpler than performing a CQ in terms of the BFCG theory variables and it can also help to understand the quantization based on a spin-foam basis, which is a categorical generalization of the spin-network basis.
Descrição
Tese de doutoramento, Física, Universidade de Lisboa, Faculdade de Ciências, 2017
Palavras-chave
Teses de doutoramento - 2017