English

Euler angles for G2

High Energy Physics - Theory 2009-11-11 v2 High Energy Physics - Lattice Mathematical Physics math.MP

Abstract

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.

Cite

@article{arxiv.hep-th/0503106,
  title  = {Euler angles for G2},
  author = {Sergio L. Cacciatori and Bianca L. Cerchiai and Alberto Della Vedova and Giovanni Ortenzi and Antonio Scotti},
  journal= {arXiv preprint arXiv:hep-th/0503106},
  year   = {2009}
}

Comments

21 pages, 2 figures, some misprints corrected