2009/03/02 by Yu. M. Zinoviev, Yu.M Zinoviev · 13 citations
Physics and Astronomy · #Antisymmetric relation #Antisymmetric tensor #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge symmetry #Gauge theory #Invariant (physics) #Lagrangian #Massless particle #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/04/035
published in Journal of High Energy Physics 2009(04), 035 (Springer Nature) · 7 pages, no figures
arxiv created 2009/03/02 · openalex publication_date 2009/04/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It was known for a long time that in d = 4 dimensions it is impossible to construct the Lagrangian for antisymmetric second rank spin-tensor that will be invariant under the gauge transformations with unconstrained spin-vector parameter. But recently a paper arXiv:0902.1471 appeared where gauge invariant Lagrangians for antisymmetric spin-tensors of arbitrary rank n in d > 2n were constructed using powerful BRST approach. To clarify apparent contradiction, in this note we carry a direct independent analysis of the most general first order Lagrangian for the massless antisymmetric spin-tensor of second rank. Our analysis shows that gauge invariant Lagrangian does exist but in d > 4 dimensions only, while in d = 4 this Lagrangian becomes identically zero. As a byproduct, we obtain a very simple and convenient form of this massless Lagrangian that makes deformation to AdS space and/or massive case a simple task as we explicitly show here. Moreover, this simple form admits natural and straightforward generalization on the case of massive antisymmetric spin-tensors of rank n for d > 2n.