Interactions of a massless tensor field with the mixed symmetryof the Riemann tensor. No-go results
Faculty of Physics, University of Craiova, 13 A. I. Cuza Str., 1100, Craiova, Romania
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Non-trivial, consistent interactions of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in the following cases: self-couplings, cross-interactions with a Pauli-Fierz field and cross-couplings with purely matter theories. The main results, obtained from BRST cohomological techniques under the assumptions of smoothness, locality, Lorentz covariance and Poincaré invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, can be synthesized into the following results: no consistent self-couplings exist, but a cosmological-like term; no cross-interactions with the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings with the matter theories such that the matter fields gain gauge transformations are allowed.
© Springer-Verlag, 2004