Second order differential equations for bosons with spin j > 1 and in the bases of general tensor-spinors of rank-2j
| Autor: | Guzman, V. M. Banda, Kirchbach, M. |
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| Rok vydání: | 2016 |
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| Zdroj: | Eur.Phys.J. Plus (2016) 131:313 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1140/epjp/i2016-16313-2 |
| Popis: | A boson of spin-j>1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly (j,0)+ (0,j) representation specific second order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank-2j. Comment: arXiv admin note: text overlap with arXiv:1604.06772 |
| Databáze: | arXiv |
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