Couplings between a collection of BF models and a set of three-form gauge fields

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincare invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.Comment: 17 page

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

On the generalized Freedman-Townsend model

Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of two-form gauge fields (with the Lagrangian action written in first-order form as a sum of Abelian Freedman-Townsend models) are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra. The interacting Lagrangian action contains a generalized version of non-Abelian Freedman-Townsend model. The consistency of interactions to all orders in the coupling constant unfolds certain equations, which are shown to have solutions.Comment: LaTeX, 62 page