Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations

Details Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations

2007-01-27

arxiv.org/abs/hep-th/0701253v2

Phys.Rev.D75:105010,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages; LaTex using JHEP3.cls

Scientific paper

10.1103/PhysRevD.75.105010

Dynamics with noncommutative coordinates invariant under three dimensional rotations or, if time is included, under Lorentz transformations is developed. These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3) respectively. The noncommutativity is governed by a mass parameter $M$. The principal results are: (i) a modification of the Heisenberg algebra for distances smaller than 1/M, (ii) a lower limit, 1/M, on the localizability of wave packets, (iii) discrete eigenvalues of coordinate operator in timelike directions, and (iv) an upper limit, $M$, on the mass for which free field equations have solutions. Possible restrictions on small black holes is discussed.

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