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Reply to David
November 21, 2008
by Anonymous,
1 year 5 days ago
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Hi David,
came across your comment. In fact the example is of the `lie algebra' type
that you suggest just that many of the components of the tensor C are
zero. The idea that classically you can rotate among the x,y,z,t is
expressed as a symmetry of the Lorentz group SO(3,1) and that there is
no preferred origin (point 0,0,0,0) combines with this as the statement of invariance under the Poincare group.All of this seems to be lost but is still there in the model but now as a quantum Poincare symmetry. For that, see a later
post on quantum symmetry. Its perfectly possible to have models with
x,y,z noncommuting but the simplest ones have t commuting with x,y,z; sort of complementary. Its possible to have `fully mixed up' examples but I dont know a good one which keeps Poincare symmetry as a group or quantum group. At the moment most attention is just on the simplest models for practical reasons.