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Higher Spin Fields in Siegel Space, Currents and Theta Functions | | O.A.Gelfond
; M.A.Vasiliev
; | | Date: |
16 Jan 2008 | | Abstract: | Dynamics of four-dimensional massless fields of all spins is formulated in
the Siegel space of complex $4 imes 4$ symmetric matrices. It is shown that
the unfolded equations of free massless fields, that have a form of
multidimensional Schrodinger equations, naturally distinguish between positive-
and negative-frequency solutions of relativistic field equations, i.e.
particles and antiparticles. Multidimensional Riemann theta functions are shown
to solve massless field equations in the Siegel space. We establish the
correspondence between conserved higher-spin currents in four-dimensional
Minkowski space and those in the ten-dimensional matrix space. It is shown that
global symmetry parameters of the current in the matrix space should be
singular to reproduce a nonzero current in Minkowski space. The $D$-function
integral evolution formulae for 4d massless fields in the Fock-Siegel space are
obtained. The generalization of the proposed scheme to higher dimensions and
systems of higher ranks is considered. | | Source: | arXiv, 0801.2191 | | Services: | Forum | Review | PDF | Favorites | |
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