Finsler spinoptics

Communications in Mathematical Physics

Volumn 283, Issue 3, 2008, Pages 701-727

  Duval, C ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50249093745     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0573-7     Document Type: Article

References (42)

1. Abate, M., Patrizio, G.: Finsler Metrics -A Global Approach, LNM 1591, Berlin-Heidelberg-New York: Springer-Verlag, 1994
2. Alvarez Paiva, J.C.: Some problems on Finsler geometry. In: Handbook of differential geometry. Vol. II, Dillen, F., Verstraelen, L. (eds.), Amsterdam: Elsevier, 2005
3. Antonelli P.L., Ingarden R.S., Matsumoto M.: The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. Kluwer Academic Press, Boston (1993)
4. Bejancu A., Farran H.R.: A Geometric Characterization of Finsler Manifolds of Constant Curvature K = 1. Internat. J. Math. & Math. Sci. 23(6), 399-407 (2000)
5. Bao, D., Chern, S.-S., Shen, Z.: On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces. In: Finsler Geometry, Bao, D., Chern, S.-S., Shen, Z. (eds.), Contemporary Mathematics 196, Providence, RI: Amer. Math. Soc., 1996
6. Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler Geometry. GTM 200, New York: Springer 2000
7. Bao, D., Robles, C. Ricci and Flag Curvatures in Finsler Geometry. In: A Sampler of Riemann-Finsler Geometry, Bao, D., Bryant, R.L., Chern, S.-S., Shen, Z. (eds.), MSRI Publications 50, Cambridge: Cambridge University Press, 2004
8. Berry M.V.: Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45-57 (1984)
9. Bliokh K.Yu.: Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect. Phys. Rev. Lett. 97, 043901 (2006)
10. Bliokh K.Yu., Bliokh Yu.P.: Topological spin transport of photons: the optical Magnus Effect and Berry Phase. Phys. Lett. A 333, 181-186 (2004)
11. Bliokh K.Yu., Bliokh Yu.P.: Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect. Phys. Rev. E 70, 026605 (2004)
12. Bliokh K.Yu., Bliokh Yu.P.: Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of Electromagnetic Wave Packet. Phys. Rev. Lett. 96, 073903 (2006)
13. Bliokh K.Yu., Frolov D.Yu., Kravtsov Yu.A.: Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium. Phys. Rev. A 75, 053821 (2007)
14. Born M., Wolf E.: Principles of optics. Cambridge University Press, Cambridge (1999)
15. Caponio, E., Javaloyes, M.A., Masiello, A.: Variational properties of geodesics in non-reversible Finsler manifolds and applications. http://arxiv.org/abs/math/0702323, 2007
16. Cariñena J.F., Nasarre N.: On the symplectic structure arising in geometric optics. Fortschr. Phys. 44, 181-198 (1996)
17. Cariñena J.F., Nasarre N.: Presymplectic geometry and Fermat's principle for anisotropic media. J. Phys. A 29, 1695-1702 (1996)
18. Cartan E.: Les espaces de Finsler. Hermann, Paris (1934)
19. Chern, S.-S.: Riemannian geometry as a special case of Finsler geometry. In: Finsler Geometry, Bao, D., Chern, S.-S., Shen, Z. (eds.), Contemporary Mathematics 196, Providence, RI: Amer. Math. Soc., 1996
20. Chern S.-S.: Finsler Geometry Is Just Riemannian Geometry without the Quadratic Restriction. Not. Amer. Math. Soc. 43(9), 959-963 (1996)
21. Duval C., Horváth Z., Horváthy P.: Geometrical Spinoptics and the Optical Hall Effect. J. Geom. Phys. 57, 925-941 (2007)
22. Duval C., Horváth Z., Horváthy P.: Fermat Principle for spinning light and the Optical Hall effect. Phys. Rev. D 74, 021701 (R) (2006)
23. Foulon P.: Géométrie des équations différentielles du second ordre. Ann. Inst. Henri Poincaré 45(1), 1-28 (1986)
24. Gosselin P., Bérard A., Mohrbach H.: Spin Hall effect of Photons in a Static Gravitational Field. Phys. Rev. D 75, 084035 (2007)
25. Guillemin V., Sternberg S.: Symplectic techniques in physics. Cambridge University Press, Cambridge (1984)
26. Gutkin E., Tabachnikov S.: Billiards in Finsler and Minkowski geometries. J. Geom. Phys. 40, 277-301 (2002)
27. Iglesias P.: Symétries et moment. Hermann, Paris (2000)
28. Ingarden, R.: On physical applications of Finsler geometry. In: Finsler Geometry, Bao, D., Chern, S.-S., Shen, Z. (eds.), Contemporary Mathematics 196, Providence, RI: Amer. Math. Soc., 1996
29. Kravtsov Yu.A., Bieg B., Bliokh K.Yu.: Stokes-vector evolution in a weakly anisotropic inhomogeneous medium. J. Opt. Soc. Am. A 24, 3388-3403 (2007)
30. Knebelman M.S.: Conformal geometry of generalized metric spaces. Proc. Nat. Acad. Sci. USA 15, 376-379 (1929)
31. Künzle H.P.: Canonical dynamics of spinning particles in gravitational and electromagnetic fields. J. Math. Phys. 13, 739-744 (1972)
32. Marsden J.-E., Ratiu T.: Introduction to Mechanics and Symmetry. Springer, Berlin-Heidelberg-New York (1999)
33. Onoda M., Murakami S., Nagaosa N.: Hall Effect of Light. Phys. Rev. Lett. 93, 083901 (2004)
34. Onoda M., Murakami S., Nagaosa N.: Geometrical Aspects in Optical Wavepackets Dynamics. Phys. Rev. E 74, 066610 (2006)
35. Perlick V.: Fermat principle in Finsler spacetimes. Gen. Relativ. Gravit. 38(2), 365-380 (2006)
36. Rund H.: The differential geometry of Finsler spaces. Springer Verlag, Berlin-Heidelberg-New York (1959)
37. Segre S.E., Zanza V.: Derivation of the pure Faraday and Cotton-Mouton effects when polarimetric effects in a tokamak are large. Plasma Phys. Control. Fusion 48, 1-13 (2006)
38. Shen, Z.: Landsberg Curvature, S-Curvature and Riemann Curvature. In: A Sampler of Riemann-Finsler Geometry, Bao, D., Bryant, R.L., Chern, S.-S., Shen, Z. (eds.), MSRI Publications 50, Cambridge: Cambridge University Press, 2004
39. Souriau, J.-M.: Structure des systèmes dynamiques, Paris: Dunod, 1970, ©1969; Structure of Dynamical Systems. A Symplectic View of Physics, translated by C.H. Cushman-de Vries, (R.H. Cushman, G.M. Tuynman, Translation eds.), Basel-Boston: Birkhäuser, 1997
40. Souriau J.-M.: Modèle de particule à spin dans le champ électromagnétique et gravitationnel. Ann. Inst. Henri Poincaré 20A, 315-364 (1974)
41. Sternberg, S.: On the Role of Field Theories in our Physical Conception of Geometry. In: Proc. 2nd Bonn Conf. Diff. Geom. Meths. in Math. Phys, Lecture Notes in Mathematics, 676, Berlin-Heidelberg- New York: Springer-Verlag, 1978, pp. 1-80
42. van Tiggelen B.A.: Transverse diffusion of light in Faraday-Active Media. Phys. Rev. Lett. 75, 422-424 (1995)