Gauge transformations as Lorentz-Boosted rotations

Han, D.; Kim, Y.S.; Son, D.

doi:10.1016/0370-2693(83)90509-9

Cited by 35 publications

(14 citation statements)

References 6 publications

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“…The answer given by Wigner is nothing: if the translation generators had a physical effect, the little-group representation would be infinite dimensional and the particle being described would have "continuous spin" -a property possessed by no known particle. Indeed the Wigner translations have no effect when applied to plane-wave solutions of the massless Dirac equation, and act as gauge transformations when applied to the vector potentials of plane-wave solutions of Maxwell's equations [2]. Consequently they act as the identity on the momentum eigenstates created by the operator-valued coefficients of the plane-wave modes, thus ensuring that the spin of a massless particle is entirely specified by a finite-dimensional representation of the SO(2) helicity subgroup [3].…”

Section: Introductionmentioning

confidence: 99%

Wigner Translations and the Observer Dependence of the Position of Massless Spinning Particles

2015

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The Wigner little group for massless particles is isomorphic to the Euclidean group SE(2).Applied to momentum eigenstates, or to infinite plane waves, the Euclidean "Wigner translations" act as the identity. We show that when applied to finite wavepackets the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle's helicity.We relate this effect to the spin Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.

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Section: Introductionmentioning

confidence: 99%

Wigner Translations and the Observer Dependence of the Position of Massless Spinning Particles

2015

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“…This means that there is another set of commutation relations, where K i is replaced withK i = −K i . Let us go back to the expression of Equation (2). This transition to the dotted representation is achieved by the space inversion or by the parity operation.…”

Section: Parity Time Reversal and Charge Conjugationmentioning

confidence: 99%

“…In Section 5, it is shown possible to construct transfor- The sphere corresponds to the O(3)-like little group for the massive particle. There is a plane tangential to the sphere at its north pole, which is E (2). There is also a cylinder tangent to the sphere at its equatorial belt.…”

Section: Introductionmentioning

confidence: 99%

Loop Representation of Wigner’s Little Groups

2017

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Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathematical forms for massive and for massless particles. However, it is shown possible to construct one unified representation using a graphical description. This graphical approach allows us to describe vividly parity, time reversal, and charge conjugation of the internal symmetry groups. As for the language of group theory, the two-by-two representation is used throughout the paper. While this two-by-two representation is for spin-1/2 particles, it is shown possible to construct the representations for spin-0 particles, spin-1 particles, as well as for higher-spin particles, for both massive and massless cases. It is shown also that the four-by-four Dirac matrices constitute a two-by-two representation of Wigner's little group.

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“…While the O(3)-like and E(2)-like little groups are different, it is possible to derive the latter as a Lorentz-boosted O(3)-like little group in the infinite-momentum limit. It is shown then that the two rotational degrees of freedom perpendicular momentum become one gauge degree of freedom [4].…”

Section: Introductionmentioning

confidence: 99%

Wigner’s Little Groups

2018

New Perspectives on Einstein's E = Mc²

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Wigner's little groups are subgroups of the Lorentz group dictating the internal space-time symmetries of massive and massless particles. The little group for the massive particle is like O(3) or the three-dimensional rotation group, and the little group for the massless particle is E(2) or the two-dimensional Euclidean group consisting of rotations and translations on a two-dimensional plane. While

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Gauge transformations as Lorentz-Boosted rotations

Cited by 35 publications

References 6 publications

Wigner Translations and the Observer Dependence of the Position of Massless Spinning Particles

Wigner Translations and the Observer Dependence of the Position of Massless Spinning Particles

Loop Representation of Wigner’s Little Groups

Wigner’s Little Groups

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