Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-01-15
JHEP 0903:125,2009
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 38 pages, v.3: clarifications, acknowledgements and references added, typos corrected, v.4: more comments and reference
Scientific paper
10.1088/1126-6708/2009/03/125
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ 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.
Gelfond O. A.
Vasiliev Mikhail A.
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