Biblioteca Allievi della Scuola Superiore di Catania

Contents:

Dissertation note: Tesi di diploma di 2° livello per la Classe delle Scienze Sperimentali Diploma di 2° livello Scuola Superiore di Catania, Catania, Italy 2013 A.A. 2012/2013 Abstract: What is space? What is time? These and many other questions have always puzzled philosophers and physicists of all times. Possible answers have deeply changed during the century and are still evolving towards a deeper comprehension of the fundamental laws of nature. Before giving a short plan of the thesis let us focus on the problem of Quantum Gravity. Our current knowledge on the elementary structure of nature lies on two theories: Quantum Theory, in particular the Standard Model of particle physics, and General Relativity. These theories appear to agree with almost all present observations. However there are physical situations where they lack of predictive power. For instance we do not know the gravitational scattering amplitudes for two particles if the center-of-mass energy is of order of the impact parameter in Planck units, we are not able to predict what happens at the end of the evaporation of a black hole or to describe the quantum structure of spacetime at very small scale. Two different problems are raised by the current situation: Unification and Quantum Gravity. The former deals with the hope to provide a unified description of foundamental interactions. The latter addresses the problem of completing the picture and making it consistent since a coherent description of the quantum properties of the gravitational field is still missing. Loop Quantum Gravity is a tentative to formulate a complete and consistent quantum theory of gravity i.e. a consistent and complete Quantum Field Theory whose classical limit is general relativity. Its aim is to provide prediction for gravitational phenomena. The basic idea that underlies the theory is to take seriously the characteristic features of QFT as well as that of General Relativity by merging the general-relativistic understanding of spacetime into the framework of quantum eld theory. One of the most important aspects of any QFT describing a fundamental interaction is renormalizability. We know however that General Relativity is not renormalizable. On the other hand the revolutionary new way to think at physical spacetime brought to us by Einstein's theory of Gravity relies on two main features: diffeomorphism invariance and background independence. Diffeomorphism invariance (also noted as general covariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artices and hence should play no role in the formulation of fundamental physical laws. Background independence means that there is no fixed background over which the dynamics is denied because geometry itself is a dynamical object. LQG successfully manages to combine these features by providing a diffeomorphism-invariant and background-independent tentative quantum theory of the gravitational interaction which also turns out to be ultraviolet finite. Despite its successes, however, the picture is still very far from being complete and many problems are still open. In particular one of the main questions concerns the characterization of the LQG physical Hilbert space of states and the implementation of the dynamics from the canonical formulation of the theory. The effort to provide a reasonable solution to this problem has opened the way to new compelling research lines as for example the spin foam formalism which is a tentative definition of the dynamics from the proper analogue of the functional integral for general relativity. Moreover the theory has grown up very fast in the last ten years and several remarkable and encouraging results have been found.
1. Introduction -- 2. Hamiltonian analysis of General Relativity -- 3. Loop Quantum Gravity and Spin foam Models -- 4. The Graviton Propagator in Loop Quantum Gravity and Spin foams -- 5. Concluding Remarks -- Acknowledgements -- References.

Location | Call number | Copy number | Status | Date due |
---|---|---|---|---|

Sala B : Armadio Tesi | THS_2013 530.11 F515 (Browse shelf) | 1 | Available | |

Sala B : Armadio Tesi | THS_2013 530.11 F515 (Browse shelf) | 2 | Available |

Tesi di diploma di 2° livello per la Classe delle Scienze Sperimentali Diploma di 2° livello Scuola Superiore di Catania, Catania, Italy 2013 A.A. 2012/2013

Includes bibliographical references (p. 82-86).

1. Introduction -- 2. Hamiltonian analysis of General Relativity -- 3. Loop Quantum Gravity and Spin foam Models -- 4. The Graviton Propagator in Loop Quantum Gravity and Spin foams -- 5. Concluding Remarks -- Acknowledgements -- References.

Tesi discussa il 16/12/2013.

What is space? What is time? These and many other questions have always puzzled philosophers and physicists of all times. Possible answers have deeply changed during the century and are still evolving towards a deeper comprehension of the fundamental laws of nature. Before giving a short plan of the thesis let us focus on the problem of Quantum Gravity. Our current knowledge on the elementary structure of nature lies on two theories: Quantum Theory, in particular the Standard Model of particle physics, and General Relativity. These theories appear to agree with almost all present observations. However there are physical situations where they lack of predictive power. For instance we do not know the gravitational scattering amplitudes for two particles if the center-of-mass energy is of order of the impact parameter in Planck units, we are not able to predict what happens at the end of the evaporation of a black hole or to describe the quantum structure of spacetime at very small scale. Two different problems are raised by the current situation: Unification and Quantum Gravity. The former deals with the hope to provide a unified description of foundamental interactions. The latter addresses the problem of completing the picture and making it consistent since a coherent description of the quantum properties of the gravitational field is still missing. Loop Quantum Gravity is a tentative to formulate a complete and consistent quantum theory of gravity i.e. a consistent and complete Quantum Field Theory whose classical limit is general relativity. Its aim is to provide prediction for gravitational phenomena. The basic idea that underlies the theory is to take seriously the characteristic features of QFT as well as that of General Relativity by merging the general-relativistic understanding of spacetime into the framework of quantum eld theory. One of the most important aspects of any QFT describing a fundamental interaction is renormalizability. We know however that General Relativity is not renormalizable. On the other hand the revolutionary new way to think at physical spacetime brought to us by Einstein's theory of Gravity relies on two main features: diffeomorphism invariance and background independence. Diffeomorphism invariance (also noted as general covariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artices and hence should play no role in the formulation of fundamental physical laws. Background independence means that there is no fixed background over which the dynamics is denied because geometry itself is a dynamical object. LQG successfully manages to combine these features by providing a diffeomorphism-invariant and background-independent tentative quantum theory of the gravitational interaction which also turns out to be ultraviolet finite. Despite its successes, however, the picture is still very far from being complete and many problems are still open. In particular one of the main questions concerns the characterization of the LQG physical Hilbert space of states and the implementation of the dynamics from the canonical formulation of the theory. The effort to provide a reasonable solution to this problem has opened the way to new compelling research lines as for example the spin foam formalism which is a tentative definition of the dynamics from the proper analogue of the functional integral for general relativity. Moreover the theory has grown up very fast in the last ten years and several remarkable and encouraging results have been found.