This thesis is devoted to the study of different formulations of General Relativity (GR) as a a fundamental theory of the gravitational interaction in the setting of Cattaneo, Mnev and Reshetikhin (CMR) on manifolds with boundary. The Batalin (Fradkin) Vilkovisky formalisms (BV and BFV) were joined by CMR to associate to a BV gauge theory on a space-time manifold $ \mathit{M}$ a correspondent BFV structure on its boundary $\partial \mathit{M}$, and a set of axioms for general gauge theories was proposed in this context, in order to have a neat quantisation scheme.

The present work is aimed at testing the axioms on different, classically equivalent formulations of General Relativity, namely the Einstein Hilbert metric theory of gravity, the Palatini Holst tetrad formulation of GR and two BF-like theories that go under the name of Plebanski action8 and McDowell-Mansouri action9.

We prove that only some of these formulations satisfy the CMR axioms, thus inducing a BV-BFV theory: the Einstein Hilbert theory, for all manifolds with boundary of dimension $ \mathit{d}$ + 1 $ \ne$ 2 with spacelike or timelke boundary components, and the BF-formulation of the McDowell-Mansoury action, under some natural regularity assumptions on the field $ \mathit{B}$. The classical canonical analysis for the Einstein Hilbert and the Palatini Holst actions is also discussed, and we show how the machinery is capable of recovering known results in a straightforward way, yielding in addition an explicit symplectic characterisation of the phase space of the theory. This is a first step in the programme of CMR quantisation of gauge theories on manifolds with boundary, applied to the fundamental, and still open case of General Relativity.

Schiavina, Michele. *BV-BFV approach to general relativity.* 2015, University of Zurich, Faculty of Science.

## Abstract

This thesis is devoted to the study of different formulations of General Relativity (GR) as a a fundamental theory of the gravitational interaction in the setting of Cattaneo, Mnev and Reshetikhin (CMR) on manifolds with boundary. The Batalin (Fradkin) Vilkovisky formalisms (BV and BFV) were joined by CMR to associate to a BV gauge theory on a space-time manifold $ \mathit{M}$ a correspondent BFV structure on its boundary $\partial \mathit{M}$, and a set of axioms for general gauge theories was proposed in this context, in order to have a neat quantisation scheme.

The present work is aimed at testing the axioms on different, classically equivalent formulations of General Relativity, namely the Einstein Hilbert metric theory of gravity, the Palatini Holst tetrad formulation of GR and two BF-like theories that go under the name of Plebanski action8 and McDowell-Mansouri action9.

We prove that only some of these formulations satisfy the CMR axioms, thus inducing a BV-BFV theory: the Einstein Hilbert theory, for all manifolds with boundary of dimension $ \mathit{d}$ + 1 $ \ne$ 2 with spacelike or timelke boundary components, and the BF-formulation of the McDowell-Mansoury action, under some natural regularity assumptions on the field $ \mathit{B}$. The classical canonical analysis for the Einstein Hilbert and the Palatini Holst actions is also discussed, and we show how the machinery is capable of recovering known results in a straightforward way, yielding in addition an explicit symplectic characterisation of the phase space of the theory. This is a first step in the programme of CMR quantisation of gauge theories on manifolds with boundary, applied to the fundamental, and still open case of General Relativity.

## Downloads

0 downloads since 12 months

## Additional indexing

Item Type: | Dissertation |
---|---|

Referees: | Cattaneo Alberto S, De Lellis Camillo, Willwacher Thomas |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2015 |

Deposited On: | 18 Feb 2016 10:57 |

Last Modified: | 22 Sep 2016 11:44 |

Number of Pages: | 159 |

Official URL: | http://www.recherche-portal.ch/ZAD:default_scope:ebi01_prod010591850 |

## Download

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.