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Geometric Approaches to Quantum Field Theory

Geometric Approaches to Quantum Field Theory

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The ancient Greeks believed that geometry could describe everything in the Universe, and this thesis takes steps to achieve this by introducing geometric descriptions of quantum gravity, fermionic particles, and the origins of the Universe. It extends previous work to include theories with spin ½ and spin 2 degrees of freedom and introduces a geometric description of the potential term in a quantum field theory through the Eisenhart lift. The methods are applied to the theory of inflation, showing how geometry can help answer long-standing questions about the initial conditions of the Universe.

Format: Paperback / softback
Length: 202 pages
Publication date: 08 October 2022
Publisher: Springer Nature Switzerland AG


The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realizing 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 realizing 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.

Weight: 349g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030852719
Edition number: 1st ed. 2021

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