An infinite-component free field carrying compounds lying on a Regge trajectory

Abstract

One herein constructs an infinite-component generalized free field ϕ(x) which carries an infinite tower of unstable (excepting the lowest-mass member) self-compounds which is defined by a spin trajectory. ϕ(x) transforms locally under the Poincare group. The norm or propagator of ϕ(x) can be written as an infinite partial (in spinj) series of contributions of positive-definite metric, which, with the suggested constraint on the mass2 (squared) functionmj2 as |j|→∞, permits summation by the Sommerfeld-Watson transformation. In close analogy to the Gupta-Bleuler form of quantum electrodynamics, the consequent Reggeized propagator then involves contributions of indefinite metric completely equivalent to the positive-metric partial series. The indefinite metric is here directly associated with the instability of the higher Regge poles. The constraint onmj2 together with the effect of invariance underTP for the ϕ propagator leads to a particular dispersion relation for our mass2 functionmΛZ2. The latter involves Λ=(j+1/2)2,Z=P2 the fourmomentum squared, on a completely reciprocal basis. It also, necessarily, introduces two mass2 continua (r>4m02,r<0). The latter, tachyon component suggests that ϕ has to be interpreted as a fundamental field which is not directly observed. The phenomenological field having no tachyon component and which is directly observed will be discussed on the basis of unitarity in a subsequent paper. The propagator of the free field ϕ clearly obeys unitarity in a trivial way in terms of the free states defined by itself.