Towards a unified nonlinear theory of massless bosons

Abstract

Conceptual problems such as unphysical states and indefinite metric in conventional quantum electrodynamics are known to arise from the use of only the compact 0(2) subgroup of the full non-compact little group for massless particles, which is isomorphic to the two-dimensional Euclidean group E(2). We attempt to avoid these difficulties by proposing that elementary massless boson states transform as a faithful nonlinear realization of the full little group E(2) over the physically observed helicity states (photons, gravitons) corresponding to the linearly represented 0 (2) subgroup. Gravitons are necessarily unified with photons in this scheme: photons and gravitons may be regarded as Lorentz-transformable aspects of the same entity. The formulation deals with creation operators of momentum eigenstates. Nonlinear transformation laws are constructed in terms of commutator functions obtained by solving the Jacobi identity.