Skip to main content
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

Noncommutative coordinates invariant under rotations and Lorentz transformations


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 the 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 are discussed. © 2007 The American Physical Society.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View