Date of this Version
Physical Review D, VOLUME 31, NUMBER 6, 15 MARCH 1985
To be a self-contained theory, topological particle theory should explain from the basis of its own stated framework of assumptions (nonlinear self-consistency equations, pole factorization, crossing symmetry, and Hermitian analyticity} all the mathematical properties and numerical values of scattering amplitudes. This paper attempts to move the theory in this direction by showing that the phases of the zero-entropy amplitudes in the theory are, in fact, determined by the above framework of assumptions except for trivial ambiguities that appear to have no physical consequences. This extends previous work on this subject and removes the need for certain extra assumptions. Once the results in this paper have been established it can be shown that the conventional connection between spin and statistics as well as parity, time-reversal, and charge-conjugation invariance in strong interactions also follow from the above framework of assumptions. These latter results will be fully discussed in the following paper.