Tachyons and Representations of SO(2,3)

TL;DR

This paper explores embeddings of the Poincare algebra into SO(2,3) and its higher-dimensional analogs, linking group representations to tachyonic states and extending the mathematical framework of anti-de Sitter space.

Contribution

It introduces new embeddings of the Poincare algebra into SO(2,3) and higher groups, connecting these to unitary, tachyonic representations and generalizing previous results.

Findings

Embedded Poincare algebra into SO(2,3) and higher groups.

Connected unitary, tachyonic representations to these embeddings.

Extended results to q-generalizations of the groups.

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.