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arXiv · 1006.3005

Extension of the Poincar\'e Group and Non-Abelian Tensor Gauge Fields

George Savvidy
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Abstract

In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an extension of the Poincar\'e group with infinitely many generators which carry internal and space-time indices. This is similar to the super-symmetric extension of the Poincar\'e group, where instead of an anti-commuting spinor variable one should introduce a new vector variable. The construction of irreducible representations of the extended Poincar\'e algebra identifies a vector variable with the derivative of the Pauli-Lubanski vector over its length. As a result of this identification the generators of the gauge group have nonzero components only in the plane transversal to the momentum and are projecting out non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite space-like components.

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George Savvidy. 2010-06-15. Extension of the Poincar\'e Group and Non-Abelian Tensor Gauge Fields. https://doi.org/10.1142/s0217751x10051050

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