Wigner's little group and Berry's phase for massless particles

Netanel H. Lindner*, Asher Peres, Daniel R. Terno

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


The 'little group' for massless particles (namely, the Lorentz transformations A that leave a null vector invariant) is isomorphic to the Euclidean group E2: translations and rotations in a plane. We show how to obtain explicitly the rotation angle of E2 as a function of A and we relate that angle to Berry's topological phase. Some particles admit both signs of helicity, and it is then possible to define a reduced density matrix for their polarization. However, that density matrix is physically meaningless because it has no transformation law under the Lorentz group, even under ordinary rotations.

Original languageEnglish
Pages (from-to)L449–L454
Number of pages6
JournalJournal of Physics A: Mathematical and General
Issue number29
Publication statusPublished - 25 Jul 2003
Externally publishedYes


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