From Poincare to affine invariance

doi:10.1088/0264-9381/19/12/305

From Poincaré to affine invariance: how does the Dirac equation generalize?

Ingo Kirsch et al 2002 Class. Quantum Grav. 19 3157-3178 doi: 10.1088/0264-9381/19/12/305

PDF (293 KB) | Gzipped PS (305 KB) | References | Articles citing this article

Ingo Kirsch^1,3 and Djordje Sijacki²
¹ Institute of Theoretical Physics, University of Cologne, 50923 Köln, Germany
² Institute of Physics, PO Box 57, 11001 Belgrade, Yugoslavia
E-mail: ik@physik.hu-berlin.de and sijacki@phy.bg.ac.yu
³ Present address: Humboldt-Universität zu Berlin, Institut für Physik, D-10115 Berlin, Germany.

Abstract. A generalization of the Dirac equation to the case of affine symmetry, with $\overline{SL}(4,\Bbb{R}$ replacing $\overline{SO}(1,3)$ , is considered. A detailed analysis of a Dirac-type Poincaré-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component $\overline{SL}(4,\Bbb{R}$ fermionic fields, the constraints on the $\overline{SL}(4,\Bbb{R}$ vector-operator generalizing Dirac's γ matrices, as well as the minimal coupling to (metric-)affine gravity are studied. Finally, a symmetry breaking scenario for $\overline{SA}(4,\Bbb{R}$ is presented which preserves the Poincaré symmetry.

PACS numbers: 0365P, 0462

Print publication: Issue 12 (21 June 2002)
Received 4 December 2001
Published 27 May 2002

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

From Poincaré to affine invariance: how does the Dirac equation generalize?

Find related articles

Article options

Authors & Referees