Quadratic s-form field actions with semi-bounded energy

Abstract

We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the YangMills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gravity in four space-time dimensions even in the presence of a Minkowskian metric background.  2001 Elsevier Science B.V. All rights reserved.

Kinetic terms for 2-forms in four dimensions

“…It is thus necessary to find a way to classify the possible kinetic terms according to their particle contents and their physical consistency (in particular it is very important to know if their energy is semibounded or not). In two previous papers [1], [2] we have obtained some partial results in this direction. In [1] we classified all the possible diff-invariant terms in four dimensions.…”

“…If we could find helicity 2 states, we would have an alternative to the Fierz-Pauli Lagrangian that might lead to a reasonable perturbative quantum field theory of gravity after the introduction of self-interactions and matter couplings. The results of [2] show that the action (1) for 2-forms does not work in this sense; once we impose the condition that the energy be semi-definite we find out that it describes only massless scalars. However, as already quoted above, for 2-forms there is the possibility of adding an extra term to (1).…”

“…One of the interesting results of that paper was finding out that quadratic diff-invariant Lagrangians do not describe any local physical degrees of freedom. In [2] we studied a family of quadratic actions for s-form fields in Minkowski spacetime 2 given by…”

“…We study this problem within the covariant symplectic framework introduced by Crnković and Witten [6,7,8] and used by the authors in [1,2,9]. The method followed in those papers involved two main steps: the solution of the field equations and the evaluation, on the solution space, of the symplectic form derived from the action.…”

“…The process of solving the field equations depends on the geometrical setting of the problem. In the case of the diff-invariant actions considered in [1,9] they could be solved in a straightforward way, however, in the presence of a Minkowskian background [2] the process was more involved. It consisted of three main steps: the identification of the relevant algebraic sectors, the obtention of differential necessary conditions and, finally, the resolution of the field equations.…”