Geometric Approaches to Quantum Field Theory
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Beschreibung
The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself.
The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin ½ and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe.
This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.
The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself.
The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin ½ and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe.
This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.
Nominated as an outstanding Ph.D. thesis by The University of Manchester, Manchester, United Kingdom Provides a comprehensive introduction to the increasingly popular topic of field space covariance Includes an in-depth discussion of the initial conditions problem of inflation
Autor*in
Kieran Finn
Themen in »Geometric Approaches to Quantum Field Theory«
Quantum Field Theory Inflation Field Space Vilkovisky DeWitt Cosmological Frame Problem Initial Conditions Quantum Gravity Supermanifold