Tachyons and virtual fields for elementary particles in strong interactions. Part 1

An infinite component free field is constructed and carries an infinite tower of unstable selfcompounds which is defined by a mass-squared trajectory. The field transforms locally under the Poincare group, being a direct sum of spinor representations. The norm or propagator of the field can be written as an infinite partial series (in spin j) of contributions of positive definite metric, which permits transformation to a Regge pole plus background contribution. The Regge pole dominates in the relativistic domain p→infinity. The associated continuation to complex j values introduces an indefinite metric into the propagator and has associated oscillatory characteristic functions of the spinor representation. The constraint on the mass-squared function permits the propogator to be written in terms of partial propagators such that the resonances appear in the correct position on the second z sheet and the Regge poles in the correct Regge j-quadrants. The partial propagator can be written in a TCP invariant form in terms of a spectral function determined by the dispersion integral for a particular condition on the mass-squared trajectory and involving continua of the real mass-squared variable r (r>=4m20 and r<=0 where m0 is the stable mass corresponding to spin j=0). This allows the complete infinite component free field corresponding to the real mass-squared and spin spectrum to be constructed in such a way that it transforms locally under Lorentz transformatons and has a propagator which has the right resonances and motion of Regge poles. Since there is one mass spectral function, the field should be considered in toto and as a fully virtual field, and furthermore as a possible solution of nonlinear field equation of motion. The tachyonic field component r<=0 of the field has a noncanonical commutation rule with some analogy to those associated with the Coulomb interaction in quantum electrodynamics