Gauge Invariance for Classical Massless Particles with Spin


Wigner’s quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle version of the Higgs mechanism.

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    For a more comprehensive treatment of the results in this paper, see [3].

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    For an early example of this technique, see [5]. For a more modern, pedagogical treatment, see [4].

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    See [11] for a pedagogical review.

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    For a derivation, see, for example, [3, 11].

  6. 6.

    Note that if we permit parity transformations, which map \(\sigma \mapsto -\sigma\), then we must require that the equivalence relation (49) hold only for states that share the same helicity \(\sigma\).


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J. A. B. has benefited from personal communications with Howard Georgi, Andrew Strominger, David Griffiths, David Kagan, David Morin, Logan McCarty, Monica Pate, and Alex Lupsasca.

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Correspondence to Jacob A. Barandes.

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Barandes, J.A. Gauge Invariance for Classical Massless Particles with Spin. Found Phys 51, 7 (2021).

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  • Gauge theory
  • Particle physics
  • Spin
  • Classical field theory
  • Representation theory
  • Higgs mechanism