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

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Détails bibliographiques
Auteurs principaux:	Palmerduca, Eric, Qin, Hong
Format:	Preprint
Publié:	2024
Sujets:	Mathematical Physics Quantum Physics
Accès en ligne:	Acceder al recurso
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_version_	1866916716245680128
author	Palmerduca, Eric Qin, Hong
author_facet	Palmerduca, Eric Qin, Hong
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_03494
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Helicity is a topological invariant of massless particles: C=-2h Palmerduca, Eric Qin, Hong Mathematical Physics Quantum Physics 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.
title	Helicity is a topological invariant of massless particles: C=-2h
topic	Mathematical Physics Quantum Physics
url	https://arxiv.org/abs/2407.03494

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