Relativity, Causality, Locality, Quantization and Duality in the Sp(2M) Invariant Generalized Space-Time
Abstract
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized 1/2 M(M + 1)- dimensional space-time M_M with matrix coordinates. It is shown that classical solutions of these field equations define a causal structure in M_M and admit a well-defined decomposition into positive and negative frequency solutions that allows consistent quantization in a positive definite Hilbert space. The effect of constraints on the localizability of fields in the generalized space-time is analyzed. Usual d-dimensional Minkowski space-time is identified with the subspace of the matrix space M_M that allows true localization of the dynamical fields. Minkowski coordinates are argued to be associated with some Clifford algebra in the matrix space M_M. The dynamics of a conformal scalar and spinor in M_2 and M_4 is shown to be equivalent, respectively, to the usual conformal field dynamics of a scalar and spinor in the 3d Minkowski space-time and the dynamics of massless fields of all spins in the 4d Minkowski space-time. An extension of the electro-magnetic duality transformations to all spins is identified with a particular generalized Lorentz transformation in M_4. The M = 8 case is shown to correspond to a 6d chiral higher spin theory. The cases of M = 16 (d = 10) and M = 32 (d = 11) are discussed briefly.
- Publication:
-
Multiple Facets of Quantization and Supersymmetry: Michael Marinov Memorial Volume. Edited by OLSHANETSKY MIKHAIL & VAINSHTEIN ARKADY. Published by World Scientific Publishing Co. Pte. Ltd
- Pub Date:
- 2002
- DOI:
- 10.1142/9789812777065_0044
- arXiv:
- arXiv:hep-th/0111119
- Bibcode:
- 2002mfqs.book..826V
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- Latex, 47 pages