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      Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2)

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          Abstract

          Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we investigate the consistent cross-couplings between two collections of tensor fields with the mixed symmetries of the type (3,1) and (2,2). The computations are done with the help of the deformation theory based on a cohomological approach in the context of the antifield-BRST formalism. Our results can be synthesized in: 1. there appear consistent cross-couplings between the two types of field collections at order one and two in the coupling constant such that some of the gauge generators and of the reducibility functions are deformed, and 2. the existence or not of cross-couplings among different fields with the mixed symmetry of the Riemann tensor depends on the indefinite or respectively positive-definite behaviour of the quadratic form defined by the kinetic terms from the free Lagrangian.

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          Local BRST cohomology in the antifield formalism: I. General theorems

          We establish general theorems on the cohomology H(s|d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local p-forms depending on the fields and the antifields (=sources for the BRST variations). It is shown that Hk(s|d) is isomorphic to Hk(δ|d) in negative ghost degree k (k>0), where δ is the Koszul-Tate differential associated with the stationary surface. The cohomological group H1(δ|d) in form degree n is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group Hk(δ|d) in form degree n is isomorphic to the space of nk forms that are closed when the equations of motion hold. The groups Hk(δ|d) (k>2) are shown to vanish for standard irreducible gauge theories. The group H2(δ|d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups Hk(s|d) under the introduction of non minimal variables and of auxiliary
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            Generalized gauge fields

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              Massless particles in arbitrary representations of the Lorentz group

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                Author and article information

                Journal
                03 March 2011
                Article
                10.1142/S0217751X1004797X
                1103.0634
                ce4af3b5-2509-4771-bd9d-9e034886209b

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Int.J.Mod.Phys.A25:1211-1238,2010
                35 pages
                hep-th gr-qc

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