{"id":{"repo_id":"soton","oai_identifier":"oai:eprints.soton.ac.uk:50610"},"canonical_url":"https://search.dev.ndltd.org/etd/soton/oai:eprints.soton.ac.uk:50610","repository":{"repo_id":"soton","name":"University of Southampton","base_url":"https://eprints.soton.ac.uk/cgi/oai2"},"display":{"title":"Gravity, spinors and gauge-natural bundles","abstract":"The purpose of this thesis is to give a fully gauge-natural formulation of gravitation theory, which turns out to be essential for a correct geometrical formulation of the coupling between gravity and spinor fields. In Chapter 1 we recall the necessary background material from differential geometry and introduce the fundamental notion of a gauge-natural bundle. Chapter 2 is devoted to expounding the general theory of Lie derivatives, its specialization to the gauge-natural context and, in particular, to spinor structures. In Chapter 3 we describe the geometric approach to the calculus of variations and the theory of conserved quantities. Then, in Chapter 4 we give our gauge-natural formulation of the Einstein (-Cartan) -Dirac theory and, on applying the formalism developed in the previous chapter, derive a new gravitational superpotential, which exhibits an unexpected freedom of a functorial origin. Finally, in Chapter 5 we complete the picture by presenting the Hamiltonian counterpart of the Lagrangian formalism developed in Chapter 3, and proposing a multisymplectic derivation of bi-instantaneous dynamics. Appendices supplement the core of the thesis by providing the reader with useful background information, which would nevertheless disrupt the main development of the work. Appendix A is devoted to a concise account of categories and functors. In Appendix B we review some fundamental notions on vector fields and flows, and prove a simple, but useful, proposition. In Appendix C we collect the basic results that we need on Lie groups, Lie algebras and Lie group actions on manifolds. Finally, Appendix D consists of a short introduction to Clifford algebras and spinors.","abstract_html":"The purpose of this thesis is to give a fully gauge-natural formulation of gravitation theory, which turns out to be essential for a correct geometrical formulation of the coupling between gravity and spinor fields. In Chapter 1 we recall the necessary background material from differential geometry and introduce the fundamental notion of a gauge-natural bundle. Chapter 2 is devoted to expounding the general theory of Lie derivatives, its specialization to the gauge-natural context and, in particular, to spinor structures. In Chapter 3 we describe the geometric approach to the calculus of variations and the theory of conserved quantities. Then, in Chapter 4 we give our gauge-natural formulation of the Einstein (-Cartan) -Dirac theory and, on applying the formalism developed in the previous chapter, derive a new gravitational superpotential, which exhibits an unexpected freedom of a functorial origin. Finally, in Chapter 5 we complete the picture by presenting the Hamiltonian counterpart of the Lagrangian formalism developed in Chapter 3, and proposing a multisymplectic derivation of bi-instantaneous dynamics. Appendices supplement the core of the thesis by providing the reader with useful background information, which would nevertheless disrupt the main development of the work. Appendix A is devoted to a concise account of categories and functors. In Appendix B we review some fundamental notions on vector fields and flows, and prove a simple, but useful, proposition. In Appendix C we collect the basic results that we need on Lie groups, Lie algebras and Lie group actions on manifolds. Finally, Appendix D consists of a short introduction to Clifford algebras and spinors.","abstract_has_math":false,"creators":["Matteucci, Paolo"],"institution":"University of Southampton","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Vickers, James A."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-02","date_published":"2003-02","updated_at":"2026-07-24T04:35:50Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Vickers, James A."]},{"key":"dc:creator","label":"Author","values":["Matteucci, Paolo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2003-02"]},{"key":"dc:date.issued","label":"Date","values":["2003-02"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics (pre 2011 reorg)","Department of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Southampton"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.soton.ac.uk/50610/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.soton.ac.uk/50610/1/00247964.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to give a fully gauge-natural formulation of gravitation theory, which turns out to be essential for a correct geometrical formulation of the coupling between gravity and spinor fields. In Chapter 1 we recall the necessary background material from differential geometry and introduce the fundamental notion of a gauge-natural bundle. Chapter 2 is devoted to expounding the general theory of Lie derivatives, its specialization to the gauge-natural context and, in particular, to spinor structures. In Chapter 3 we describe the geometric approach to the calculus of variations and the theory of conserved quantities. Then, in Chapter 4 we give our gauge-natural formulation of the Einstein (-Cartan) -Dirac theory and, on applying the formalism developed in the previous chapter, derive a new gravitational superpotential, which exhibits an unexpected freedom of a functorial origin. Finally, in Chapter 5 we complete the picture by presenting the Hamiltonian counterpart of the Lagrangian formalism developed in Chapter 3, and proposing a multisymplectic derivation of bi-instantaneous dynamics. Appendices supplement the core of the thesis by providing the reader with useful background information, which would nevertheless disrupt the main development of the work. Appendix A is devoted to a concise account of categories and functors. In Appendix B we review some fundamental notions on vector fields and flows, and prove a simple, but useful, proposition. In Appendix C we collect the basic results that we need on Lie groups, Lie algebras and Lie group actions on manifolds. Finally, Appendix D consists of a short introduction to Clifford algebras and spinors."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["Gravity, spinors and gauge-natural bundles"]}]}],"canonical_facts":{"dc:contributor.advisor":["Vickers, James A."],"dc:creator":["Matteucci, Paolo"],"dc:date":["2003-02"],"dc:date.issued":["2003-02"],"dc:description.abstract":["The purpose of this thesis is to give a fully gauge-natural formulation of gravitation theory, which turns out to be essential for a correct geometrical formulation of the coupling between gravity and spinor fields. In Chapter 1 we recall the necessary background material from differential geometry and introduce the fundamental notion of a gauge-natural bundle. Chapter 2 is devoted to expounding the general theory of Lie derivatives, its specialization to the gauge-natural context and, in particular, to spinor structures. In Chapter 3 we describe the geometric approach to the calculus of variations and the theory of conserved quantities. Then, in Chapter 4 we give our gauge-natural formulation of the Einstein (-Cartan) -Dirac theory and, on applying the formalism developed in the previous chapter, derive a new gravitational superpotential, which exhibits an unexpected freedom of a functorial origin. Finally, in Chapter 5 we complete the picture by presenting the Hamiltonian counterpart of the Lagrangian formalism developed in Chapter 3, and proposing a multisymplectic derivation of bi-instantaneous dynamics. Appendices supplement the core of the thesis by providing the reader with useful background information, which would nevertheless disrupt the main development of the work. Appendix A is devoted to a concise account of categories and functors. In Appendix B we review some fundamental notions on vector fields and flows, and prove a simple, but useful, proposition. In Appendix C we collect the basic results that we need on Lie groups, Lie algebras and Lie group actions on manifolds. Finally, Appendix D consists of a short introduction to Clifford algebras and spinors."],"dc:format":["text"],"dc:identifier.uri":["https://eprints.soton.ac.uk/50610/1/00247964.pdf"],"dc:publisher.department":["Mathematics (pre 2011 reorg)","Department of Mathematics"],"dc:publisher.institution":["University of Southampton"],"dc:relation.isreferencedby":["https://eprints.soton.ac.uk/50610/"],"dc:title":["Gravity, spinors and gauge-natural bundles"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T04:35:50Z"}