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It can be achieved by considering massless representations of the 6 D Poincaré group in state space in terms of the canonically conjugate position and momentum operators, as well as the canonically conjugate pair of spinor operators. To construct infinite spin fields in six-dimensionalMinkowski space, we should describe a possible spectrum of states corresponding to these fields and, first of all, to clarify the spin structure.
the review and earlier references therein, and recent papers ) where aspects of interactions and supersymmetry of infinite spin fields have been examined).Since field realizations of the Poincaré group representations in each concrete dimension have specific features, infinite spin fields in higher dimensions deserve a separate study. The study of the infinite spin representations of the Poincaré group, their field realizations and dynamical description aroused considerable interest, which led to the formation of a certain research branch mainly in the context of the theory of higher spin fields (see e.g. Footnote 1 In this paper, we continue our study of field irreducible massless representations of the six-dimensional Poincaré group focusing on the infinite spin representations and their Lagrangian formulation. One of such aspects is a description of the massless representations of the Poincaré group in multi-dimensional spaces (see e.g. The study of various aspects of classical and quantum field theory in higher dimensions attracts attention basically due to connections with the low-energy limit of superstring theory and miraculous cancelations of some divergences in supersymmetric field models.
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