Publicação
Semiclassical limit of the EPRL spin foam model
| Resumo: | One of the pressing issues of present-day theoretical physics is the need for the quantisation of gravity. Although Einstein’s theory of general relativity (GR) has experienced tremendous success as a classical theory of gravity, it faces a number of problems, including the existence of singularities in high-curvature regimes, such as the centre of a black hole or the Big Bang. In such scenarios, quantum effects of thegeometry of spacetime are posited to play an important role, thus begging the formulation of a theoryof quantum gravity. Such an endeavour naturally leads to several different approaches, which generallytake the main assumptions from either quantum field theory or general relativity and attempt to accountfor the other a posteriori.In this dissertation, we opt for the use of general relativity as a starting point for quantising gravity andpresent the background independent non-perturbative canonical quantisation approach known as “loopquantum gravity”. From this theory, it is possible to construct objects known as “spin foams”, which allowus to explore its dynamics from a covariant perspective. More specifically, the spin foam quantization ofgeneral relativity is a path integral quantization based on the loop quantum gravity approach, where the gravitational field is described by “spin networks”. These spin networks can be understood as Wilson loop variables for the Ashtekar formulation of GR. Within the Engle-Pereira-Rovelli-Livine (EPRL) spin foam model, the transition amplitudes are constructed by using the topological gravity theory based on the BF theory for the Lorentz group and the constraints which define GR are then imposed on them. Consistency of any quantum gravity theory requires its correspondence to general relativity in the low-energy scale and this prompts us to analyse the semiclassical limit of the aforementioned EPRL model. The study of such a limit is performed through the use of the effective action approach from background field method of quantum field theory, which yields a generalisation of GR — in the sense that it allows non-metric geometries — as the semiclassical limit of the EPRL model. In other words, the leading term of the one-loop effective action of the EPRL model corresponds to the area-Regge action, which is based on the Regge action discretising gravity. Finally, after presenting the review described above, we discuss a version of Regge calculus which takes triangle areas and 3d angles as variables, define a new convergent state sum from it and extend the theory in order to include a particular type of Lorentzian triangulation. |
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| Autores principais: | Marques, Miguel João de Lopes |
| Assunto: | Espuma de spin Limite semiclássico Modelo EPRL Acção efectiva Cálculo de Regge Teses de mestrado - 2018 |
| Ano: | 2018 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | One of the pressing issues of present-day theoretical physics is the need for the quantisation of gravity. Although Einstein’s theory of general relativity (GR) has experienced tremendous success as a classical theory of gravity, it faces a number of problems, including the existence of singularities in high-curvature regimes, such as the centre of a black hole or the Big Bang. In such scenarios, quantum effects of thegeometry of spacetime are posited to play an important role, thus begging the formulation of a theoryof quantum gravity. Such an endeavour naturally leads to several different approaches, which generallytake the main assumptions from either quantum field theory or general relativity and attempt to accountfor the other a posteriori.In this dissertation, we opt for the use of general relativity as a starting point for quantising gravity andpresent the background independent non-perturbative canonical quantisation approach known as “loopquantum gravity”. From this theory, it is possible to construct objects known as “spin foams”, which allowus to explore its dynamics from a covariant perspective. More specifically, the spin foam quantization ofgeneral relativity is a path integral quantization based on the loop quantum gravity approach, where the gravitational field is described by “spin networks”. These spin networks can be understood as Wilson loop variables for the Ashtekar formulation of GR. Within the Engle-Pereira-Rovelli-Livine (EPRL) spin foam model, the transition amplitudes are constructed by using the topological gravity theory based on the BF theory for the Lorentz group and the constraints which define GR are then imposed on them. Consistency of any quantum gravity theory requires its correspondence to general relativity in the low-energy scale and this prompts us to analyse the semiclassical limit of the aforementioned EPRL model. The study of such a limit is performed through the use of the effective action approach from background field method of quantum field theory, which yields a generalisation of GR — in the sense that it allows non-metric geometries — as the semiclassical limit of the EPRL model. In other words, the leading term of the one-loop effective action of the EPRL model corresponds to the area-Regge action, which is based on the Regge action discretising gravity. Finally, after presenting the review described above, we discuss a version of Regge calculus which takes triangle areas and 3d angles as variables, define a new convergent state sum from it and extend the theory in order to include a particular type of Lorentzian triangulation. |
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