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

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

2003-04-02

arxiv.org/abs/hep-th/0304017v1

J.Phys. A36 (2003) L449

Physics

High Energy Physics

High Energy Physics - Theory

4 pages revtex

Scientific paper

10.1088/0305-4470/36/29/101

The ``little group'' for massless particles (namely, the Lorentz transformations $\Lambda$ 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 $\Lambda$ 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.

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