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An algebraic approach to physical fields

Chen, Lu and Fritz, Tobias (2021) An algebraic approach to physical fields. [Preprint]

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Abstract

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields are primitive. We explain how the theory of \emph{natural operations} in differential geometry---the modern formalism behind classifying diffeomorphism-invariant constructions---can be used to obtain concrete implementations of this idea for any given collection of fields.

For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Chen, Luluchen@ku.edu.tr
Fritz, Tobiastobias.fritz@uibk.ac.at
Additional Information: To appear in Studies in History and Philosophy of Science.
Keywords: field (physics) algebraicism Einstein algebras substantivalism natural operations dynamicism
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Tobias Fritz
Date Deposited: 18 Aug 2021 02:59
Last Modified: 18 Aug 2021 02:59
Item ID: 19448
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Symmetries/Invariances
Date: 16 August 2021
URI: http://philsci-archive.pitt.edu/id/eprint/19448

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