Casini, H.; Montemayor, R.; Urrutia, L. F. Dual theories for mixed symmetry fields. Spin-two case: \((1,1)\) versus \((2,1)\) Young symmetry type fields. (English) Zbl 0977.81159 Phys. Lett., B 507, No. 1-4, 336-344 (2001). Summary: We show that the parent Lagrangian method gives a natural generalization of the dual theories concept for non \(p\)-form fields. Using this generalization we construct here a three-parameter family of Lagrangians that are dual to the Fierz-Pauli description of a free massive spin-two system. The dual field is a three-index tensor \(T_{(\mu\nu)\rho}\), which dynamically belongs to the \((2,1)\) representation of the Lorentz group. As expected, the massless limit of our Lagrangian, which is parameter independent, has two propagating degrees of freedom per space point. Cited in 5 Documents MSC: 81T99 Quantum field theory; related classical field theories Keywords:parent Lagrangian method; Fierz-Pauli massive spin-two system description; Lorentz group representations PDFBibTeX XMLCite \textit{H. Casini} et al., Phys. Lett., B 507, No. 1--4, 336--344 (2001; Zbl 0977.81159) Full Text: DOI arXiv References: [1] Kiritsis, E., Supersymmetry and duality in field theory and string theory · Zbl 0917.53027 [2] Lund, F.; Regge, T., Phys. Rev. D, 14, 1524 (1976) [3] Kalb, M.; Ramond, P., Phys. Rev. D, 9, 2273 (1974) [4] Davis, R. L.; Shellard, E. P.S., Phys. Rev. Lett., 63, 2021 (1989) [5] Gamberg, L.; Milton, K. A., Phys. Rev. D, 61, 075013 (2000), and references therein [6] Montonen, C.; Olive, D. I., Phys. Lett. B, 72, 117 (1977) [7] Gómez, C.; Henández, R., Electric-magnetic duality and effective field theories [8] Quevedo, F.; Trugenberger, C. A., Nucl. Phys. B, 501, 143 (1997) [9] Chuscinski, D., Rep. Math. Phys., 45, 121 (2000) [10] Quevedo, F.; Trugenberger, C. A., Int. J. Mod. Phys. A, 12, 1227 (1997) [11] Hamermesh, M., Group Theory (1962), Addison Wesley · Zbl 0151.34101 [12] Labastida, J. M.F.; Morris, T. R., Phys. Lett. B, 180, 101 (1986) [13] Garcı́a, J. A.; Knaepen, B., Phys. Lett. B, 441, 198 (1998) [14] Curtright, T., Phys. Lett. B, 165, 304 (1985) [15] Troncoso, R.; Zanelli, J., Phys. Rev. D, 58, 101703 (1998) [16] Dubois-Violette, M., Lectures on differentials, generalized differentials and on some examples related to theoretical physics · Zbl 1096.18503 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.