Quadratic s-form field actions with semi-bounded energy

J.Fernando Barbero G,Eduardo J.S Villaseñor

doi:10.1016/s0550-3213(01)00059-1

Abstract

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 Yang–Mills 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.

Highlights

During the last years a great deal of effort has been devoted to the problem of describing consistent quantum field theories obtained by deformations of well known free Lagrangians such as the Maxwell action for electromagnetism and generalizations to p-forms [1,2,3], the Fierz–Pauli [4] model for spin 2 fields in a Minkowskian metric background and many others
In the previous examples the free actions considered are physically consistent because they have a semi-bounded energy and, a well defined vacuum. This feature is kept after the introduction of interaction terms, at least for small values of the coupling constant. This leads us to demand, as a first requirement, that the free actions that we study here must satisfy that the energy be semi-bounded
M is a four-dimensional pseudo-Riemannian manifold 4 without boundary with metric g that defines the Hodge dual ∗, A is a set of N 1-form fields that we write as a column vector whose transpose will be denoted by At; d is the exterior derivative, δ its dual and ∧ the usual exterior product

Summary

Introduction

During the last years a great deal of effort has been devoted to the problem of describing consistent quantum field theories obtained by deformations of well known free Lagrangians such as the Maxwell action for electromagnetism and generalizations to p-forms [1,2,3], the Fierz–Pauli [4] model for spin 2 fields in a Minkowskian metric background and many others In all these cases the starting point is the same: take several copies of a free action such as the ones quoted above and study the possible interaction terms that can be consistently added to them. The purpose of this paper is to study a rather general class of them as a step towards its complete classification.

Objectives

Findings

Conclusion