Helicity is a topological invariant of massless particles: C=-2h

Abstract

There is an elementary but indispensable relationship between the topology and geometry of massive particles. The geometric spin $s$ is related to the topological dimension of the internal space $V$ by $\dim V=2s+1$. This breaks down for massless particles, which are characterized by their helicity $h$, but all have 1D internal spaces. We show that a subtler relation exists between the topological and geometry of massless particles. Wave functions of massless particles are sections of nontrivial line bundles over the lightcone whose topology are completely characterized by their first Chern number $C$. We prove that in general $C=-2h$. In doing so, we also exhibit a method of generating all massless bundle representations via an abelian group structure of massless particles.

arXiv comment13 pages

References in corpus (17)

• Topological Insulators
• Quantum spin Hall effect of light
• The angular momentum controversy: What's it all about and does it matter?
• Topological Origin of Equatorial Waves
• Topological waves in fluids with odd viscosity
• Plasmon Weyl Degeneracies in Magnetized Plasma
• A bulk-interface correspondence for equatorial waves
• Topological Gaseous Plasmon Polariton in Realistic Plasma
• Topological phases and bulk-edge correspondence of magnetized cold plasmas
• Quantum field theory for spin operator of the photon
• Topological Langmuir-cyclotron wave
• Gravitational waves carrying orbital angular momentum
• On the transformations generated by the electromagnetic spin and orbital angular momentum operators
• The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas
• Gravitational Waves with Orbital Angular Momentum
• Photon topology
• Graviton topology

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