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Manifestly Covariant Lagrangians, Classical Particles with Spin, and the Origins of Gauge Invariance

Barandes, Jacob A. (2019) Manifestly Covariant Lagrangians, Classical Particles with Spin, and the Origins of Gauge Invariance. [Preprint]

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Abstract

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barandes, Jacob A.jacob_barandes@harvard.edu0000-0002-3740-4418
Keywords: gauge theory, particle physics, spin, classical field theory, representation theory, Higgs mechanism
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Jacob Barandes
Date Deposited: 29 Jul 2023 20:38
Last Modified: 29 Jul 2023 20:38
Item ID: 22348
Official URL: https://arxiv.org/abs/1911.08892
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: November 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/22348

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