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In this paper, we review a general technique for converting the standardLagrangian description of a classical system into a formulation that puts timeon an equal footing with the system's degrees of freedom. We show how theresulting framework anticipates key features of special relativity, includingthe signature of the Minkowski metric tensor and the special role played bytheories that are invariant under a generalized notion of Lorentztransformations. We then use this technique to revisit a classification ofclassical particle-types that mirrors Wigner's classification of quantumparticle-types in terms of irreducible representations of the Poincar\'e group,including the cases of massive particles, massless particles, and tachyons.Along the way, we see gauge invariance naturally emerge in the context ofclassical massless particles with nonzero spin, as well as study the masslesslimit of a massive particle and derive a classical-particle version of theHiggs mechanism.

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