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Relativity, Causality, Locality, Quantization and Duality in the $Sp(2M)$ Invariant Generalized SpaceTime  M.A. Vasiliev
;  Date: 
13 Nov 2001  Subject:  hepth  Abstract:  We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $half M(M+1)$dimensional spacetime $M_M$ with matrix coordinates. It is shown that classical solutions of these field equations define a causal structure in $M_M$ and admit a welldefined 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 spacetime is analyzed. Usual ddimensional Minkowski spacetime 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 spacetime and the dynamics of massless fields of all spins in the 4d Minkowski spacetime. An extension of the electromagnetic 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.  Source:  arXiv, hepth/0111119  Services:  Forum  Review  PDF  Favorites 


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