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Relativity, Causality, Locality, Quantization and Duality in the $Sp(2M)$ Invariant Generalized Space-Time | | M.A. Vasiliev
; | | Date: |
13 Nov 2001 | | Subject: | hep-th | | Abstract: | We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $half M(M+1)$-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. | | Source: | arXiv, hep-th/0111119 | | Services: | Forum | Review | PDF | Favorites | |
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