P. To, Their use in the semiclassical framework was advocated by Souriau [7]. They were overlooked by most present authors with the notable exception of Stone et al. [4], who also suggested viewing them as gauge transformations

D. T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Physical Review D, vol.87, issue.8, 2013.
DOI : 10.1103/PhysRevD.87.085016

M. Stone and V. Dwivedi, Classical version of the non-Abelian gauge anomaly, Physical Review D, vol.88, issue.4, pp.hep-th, 2013.
DOI : 10.1103/PhysRevD.88.045012

M. Stone, V. Dwivedi, and T. Zhou, Berry phase, Lorentz covariance, and anomalous velocity for Dirac and Weyl particles, Physical Review D, vol.91, issue.2, 2015.
DOI : 10.1103/PhysRevD.91.025004

J. Y. Chen, D. T. Son, M. A. Stephanov, H. U. Yee, and Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Physical Review Letters, vol.113, issue.18
DOI : 10.1103/PhysRevLett.113.182302

C. Duval and P. A. Horvathy, Chiral fermions as classical massless spinning particles, Physical Review D, vol.91, issue.4
DOI : 10.1103/PhysRevD.91.045013

URL : https://hal.archives-ouvertes.fr/hal-01015128

E. Wigner, On unitary representations of the inhomogeneous lorentz group, Nuclear Physics B - Proceedings Supplements, vol.6, pp.149-204, 1939.
DOI : 10.1016/0920-5632(89)90402-7

R. Penrose, Twistor Algebra, Journal of Mathematical Physics, vol.8, issue.2, p.345, 1967.
DOI : 10.1063/1.1705200

DOI : 10.1142/9789814327060_0023

C. Duval, On the polarizers of compact semi-simple Lie groups. Applications, Ann. Inst. Henri Poincaré, a Phys, Théor, vol.34, pp.95-115, 1981.

P. Forgacs and N. S. Manton, Space-time symmetries in gauge theories, Communications in Mathematical Physics, vol.13, issue.1, p.72, 1980.
DOI : 10.1007/BF01200108

P. Zhang and P. A. Horvathy, Anomalous Hall effect for semiclassical chiral fermions, Physics Letters A, vol.379, issue.6, pp.hep-th, 2015.
DOI : 10.1016/j.physleta.2014.12.003

P. Kosinski, Massless relativistic particles, work in progress Two-twistor particle models and free massive higher spin fields

A. O. Barut and A. J. Bracken, The Zitterbewegung and the internal geometry of the electron, Phys. Rev. D, vol.23, 1981.

A. O. Barut and N. Zanghi, Classical Model of the Dirac Electron, Physical Review Letters, vol.52, issue.23, 1984.
DOI : 10.1103/PhysRevLett.52.2009

H. Bacry, The Poincare group, the Dirac monopole and photon localisation, Journal of Physics A: Mathematical and General, vol.14, issue.4, p.73, 1981.
DOI : 10.1088/0305-4470/14/4/001

C. Duval, J. Elhadad, and G. M. Tuynman, Pukanszky's condition and symplectic induction, Journal of Differential Geometry, vol.36, issue.2, pp.331-348, 1992.
DOI : 10.4310/jdg/1214448745

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. Duval and J. Elhadad, Geometric quantization and localization of relativistic spin systems, Proc. AMS of the 1991 Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, pp.317-330, 1991.
DOI : 10.1090/conm/132/1188446

C. Duval, Z. Horváth, and P. A. Horváthy, Geometrical spinoptics and the optical Hall effect, Journal of Geometry and Physics, vol.57, issue.3, 2007.
DOI : 10.1016/j.geomphys.2006.07.003

URL : https://hal.archives-ouvertes.fr/hal-00008769

T. Curtright, D. Fairlie, and C. K. Zachos, Features of time-independent Wigner functions, Physical Review D, vol.58, issue.2, pp.25002-9711183, 1998.
DOI : 10.1103/PhysRevD.58.025002

M. Stone, V. Dwivedi, and T. Zhou, Wigner translations and the observerdependence of the position of massless spinning particles