28 research outputs found
The structure of algebraic covariant derivative curvature tensors
We use the Nash embedding theorem to construct generators for the space of
algebraic covariant derivative curvature tensors
Gauge fields in (A)dS within the unfolded approach: algebraic aspects
It has recently been shown that generalized connections of the (A)dS space
symmetry algebra provide an effective geometric and algebraic framework for all
types of gauge fields in (A)dS, both for massless and partially-massless. The
equations of motion are equipped with a nilpotent operator called
whose cohomology groups correspond to the dynamically relevant quantities like
differential gauge parameters, dynamical fields, gauge invariant field
equations, Bianchi identities etc. In the paper the -cohomology is
computed for all gauge theories of this type and the field-theoretical
interpretation is discussed. In the simplest cases the -cohomology is
equivalent to the ordinary Lie algebra cohomology.Comment: 59 pages, replaced with revised verio
Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions
Quadratic, second-order, non-local actions for tensor gauge fields
transforming in arbitrary irreducible representations of the general linear
group in D-dimensional Minkowski space are explicitly written in a compact form
by making use of Levi-Civita tensors. The field equations derived from these
actions ensure the propagation of the correct massless physical degrees of
freedom and are shown to be equivalent to non-Lagrangian local field equations
proposed previously. Moreover, these actions allow a frame-like reformulation a
la MacDowell-Mansouri, without any trace constraint in the tangent indices.Comment: LaTeX, 53 pages, no figure. Accepted for publication in
Communications in Mathematical Physics. Local Fierz-Pauli programme achieved
by completing the analysis of Labastid