Titlebook: Geometric Approaches to Quantum Field Theory; Kieran Finn Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive licen

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https://doi.org/10.1007/b138130The laws of nature should not depend on the way we choose to describe them. We should not be able to influence the predictions of a theory or the results of an experiment just by using a different notation. This seemingly obvious fact has historically had far-reaching consequences.

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Nature doesn’t care about our conventions. She doesn’t care about our coordinates, our choice of units, or the way we choose to parametrise our fields.

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The Eisenhart Lift,The potential term did not play a major role in the geometric description of QFTs developed in the previous chapters. The potential was not included in the construction of the field space, but was instead considered an external force, separate from the field-space manifold.

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Digital Redesign of Autopilots,nt tool for understanding when and why this dependence arises, known as field space covariance. We will then show how this tool will allow us to reformulate these calculations in a way that is fully reparametrisation invariant.

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https://doi.org/10.1007/978-3-030-00172-8ity of such techniques to include gravity. Covariant formulations of gravity have received a lot of attention [8–15]. However, a consensus has not yet been reached. As we shall see, when gravity is treated as a dynamical field, the parametrisation dependence of (2.88) can manifest itself in physical

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Design of Feedback Control Systems,ormalism applied just as well to fermionic degrees of freedom, they were unable to explicitly construct the field space manifold and, in particular, made no attempt to define the field space metric for such theories.

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