The first series is given by the formula They are quadratic in field strength tensors. Using these field strength tensors one can construct two infinite series of forms Ls and Cs (s = 2, 3.) invariant with respect to the transformations 8%. Which are transforming homogeneously with respect to the extended gauge transformations 8%. _l_ „cabc( Ab Ac, Ab Ac, Ab ac, Ab SIĚvXp A/j,X Avp A/j,p AvX A/xXp Av), ![]() G1iv,X - dlAvX - dvA"ßi gfa C(Al_lAVl AiiXAv) The free field theory of totally symmetric tensors of high rank were constructed in. This allows to define generalized field strength tensors Į-mail address: A priori the tensor fields have no symmetries with respect to the first index ß. Where ^ Xs (x) are totally symmetric gauge parameters, and comprises a closed algebraic structure. The extended non-Abelian gauge transformation 8% of tensor gauge fields is defined by the equations Ĩ A% = (Sab d„ gfacbA\^ b, 8 A% = (8ab gfacbAc^b sfacbA^%b, 8A The number of symmetric indices s runs from zero to infinity.1 The index a numerates the generators La of a Lie algebra. In our recent approach the gauge fields are defined as rank-(s 1) tensors Īnd they are totally symmetric with respect to the indices X1. It is appealing to extend the gauge principle so that it would define the interaction of matter fields which carry not only non-commutative internal charges, but also arbitrary spins. All rights reserved.Īrticle history: Received 21 October 2009 Accepted 25 October 2009 Available online 29 October 2009 Editor: L. We present the free field equation for the general rank-(s 1) tensor gauge field and its higher helicity solution. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity two and zero. These equations are written in terms of the first order derivatives of extended field strength tensors, similarly to the electrodynamics and Yang-Mills theory. We analyze the free field equations for the lower rank non-Abelian tensor gauge fields. Recently proposed Lagrangian for non-Abelian tensor gauge fields contains quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with dimensionless coupling constant g. Institute of Nuclear Physics, Demokritos National Research Center, Agia Paraskevi, GR-15310 Athens, Greece Solution of free field equations in non-Abelian tensor gauge field theory ![]() Contents lists available at ScienceDirect
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