Subject: High Energy Physics - Phenomenology | Physics - Fluid Dynamics | High Energy Physics - Theory | Nuclear and High Energy Physics
The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allo... View more
 G. Dunne, R. Jackiw and C. Trugenberger, Phys. Rev. D 41, 661 (1990); G. Dunne and R. Jackiw, Nucl. Phys. (Proc. Suppl.) 33C, 114 (1993); related approaches are found in C. Duval and P. Horv´athy, Phys. Lett. B479, 284 (2000) and hep-th/0106089.
 J. Lukierski, P. Stichel and W. Zakrzewski, Ann. Phys. 260, 224 (1997); V. P. Nair and A. P. Polychronakos, Phys. Lett. B505, 267 (2001); J. Gamboa, M. Loewe and J. Rojas, hep-th/0010220.
 M. Eliashvili and G. Tsitsishvili, Intl. J. Mod. Phys. B14, 1429 (2000); L. Susskind, hep-th/0101029; A. P. Polychronakos, JHEP 0104, 011 (2001), hep-th/0103013; S. Hellerman and M. Van Raamsdonk, hep-th/0103179.
 This instance of the map between a non-commuting field theory and an effective commuting field theory [N. Seiberg and E. Witten, JHEP 9909, 032 (1999)] is worked out by A. Bichl, J. Grimstrup, L. Popp, M. Schweda and R. Wulkenhaar, hep-th/0102044.
 Note that a Lorentz non-invariant Chern-Simons addition to the Maxwell Lagrange density, ∝ A · B, similarly modifies the velocity of light, but differently for the two polarizations, hence a Faraday-type rotation occurs; S. Carrol, G. B. Field, R. Jackiw, Phys. Rev. D 41, 1231 (1990); see also J. Harvey and S. Naculich, Phys. Lett. B217, 231 (1989).
M. Chaichian, M. Sheikh-Jabbari and A. Tureanu, Phys. Rev. Lett. 86, 2716 (2001); S. Carroll, J. Harvey, V. A. Kostelecky, C. Lane and T. Okamoto, hepth/0105082.
 D. Colladay and V. A. Kostelecky, Phys. Rev. D58, 116002 (1998).
 This algebra (with b = 0) was given by L. Landau, Zh. Eksp. Teor. Fiz. 11, 592 (1941) [English translation: J. Phys. USSR, 5, 71 (1941)]; for a review see ref. .
 V. Arnold, Mathematical Methods in Classical Mechanics, (Springer, New York 1978).