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arXiv · hep-th/0304017

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

Netanel H. Lindner·Asher Peres·Daniel R. Terno
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Abstract

The ``little group'' for massless particles (namely, the Lorentz transformations $Λ$ 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 $Λ$ 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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Netanel H. Lindner, Asher Peres, Daniel R. Terno. 2003-04-02. Wigner's little group and Berry's phase for massless particles. https://doi.org/10.1088/0305-4470%2F36%2F29%2F101

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