Tachyons and Representations of SO(2,3)
Abstract
We describe an embedding of the Poincare Lie algebra into an extension of the Lie field of SO(2,3) (the anti-de Sitter group). We also describe higher dimensional analogs of this embedding, which connect SO(p,q) groups to their associated motion groups (higher dimensional Poincare groups). Further some results on q generalizations of these results are given. We apply our results to certain unitary, continuous series representations of SO(2,3) associated with functions on SO(2,3)/SO(1,3). From the embedding theorem we obtain representations of the Poincare Lie algebra which are associated with unitary, tachyonic representations of the Poincare group, provided these representations are integrable to group representations.
Keywords
Cite
@article{arxiv.math-ph/0210061,
title = {Tachyons and Representations of SO(2,3)},
author = {Patrick Moylan},
journal= {arXiv preprint arXiv:math-ph/0210061},
year = {2007}
}
Comments
Reason for replacement: there is a minus sign error in Lemma 3.1 of the original version. This minus sign error led us to the false conclusion that there were skew symmetric representations of the Poincare Lie algebra associated with certain discrete series representations of SO(2,3) associated with functions on SO(2,3)/SO(1,3). Instead, it is continuous series representations of SO(2,3) which are associated with tachyonic representations of the Poincare group