No interactions for a collection of Weyl gravitons intermediated by a scalar field

The cross-couplings among several Weyl gravitons (described in the free limit by a sum of linearized Weyl actions) in the presence of a scalar field are studied with the help of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, (background) Lorentz invariance, and the preservation of the number of derivatives on each field, together with the supplementary assumption that the internal metric defined by the sum of Weyl lagrangians is positively defined, we prove that there are no consistent cross-interactions among different Weyl gravitons in the presence of a scalar field. The couplings of a single Weyl graviton to a scalar field are also discussed.Comment: 53 page

Irreducible Hamiltonian BRST symmetry for reducible first-class systems

An irreducible Hamiltonian BRST quantization method for reducible first-class systems is proposed. The general theory is illustrated on a two-stage reducible model, the link with the standard reducible BRST treatment being also emphasized.Comment: Latex 2.09, 23 pages, to appear in Int. J. Mod. Phys.

First-Class Approaches to Massive 2-Forms

Massive 2-forms are analyzed from the point of view of the Hamiltonian quantization using the gauge-unfixing approach and respectively the Batalin--Fradkin method. Both methods finally output the manifestly Lorentz covariant path integral for 1- and 2-forms with Stueckelberg coupling.Comment: 14 page

Two-dimensional interactions between a BF-type theory and a collection of vector fields

Consistent interactions that can be added to a two-dimensional, free abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.Comment: LaTeX 2e, 31 page

Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems

An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class systems based on homological arguments is proposed. The general formalism is exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page

No multi-graviton theories in the presence of a Dirac field

The cross-couplings among several massless spin-two fields (described in the free limit by a sum of Pauli-Fierz actions) in the presence of a Dirac field are investigated in the framework of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, (background) Lorentz invariance and the preservation of the number of derivatives on each field, we prove that there are no consistent cross-interactions among different gravitons in the presence of a Dirac field. The basic features of the couplings between a single Pauli-Fierz field and a Dirac field are also emphasized.Comment: 48 page

Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,R), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any non-trivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(gamma) and containing non-trivial elements from the (invariant) characteristic cohomology H^{inv}(delta|d).Comment: Latex, 50 pages, uses amssym

BRST cohomological results on the massless tensor field with the mixed symmetry of the Riemann tensor

The basic BRST cohomological properties of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in detail. It is shown that any non-trivial co-cycle from the local BRST cohomology group can be taken to stop at antighost number three, its last component belonging to the cohomology of the exterior longitudinal derivative and containing non-trivial elements from the (invariant) characteristic cohomology.Comment: 39 page

Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model

Under some plausible assumptions, we find that the dual formulation of linearized gravity in D=5 can be nontrivially coupled to the topological BF model in such a way that the interacting theory exhibits a deformed gauge algebra and some deformed, on-shell reducibility relations. Moreover, the tensor field with the mixed symmetry (2,1) gains some shift gauge transformations with parameters from the BF sector.Comment: 63 pages, accepted for publication in Eur. Phys. J.