Time-Reversal Invariance inS-Matrix Theory of Strong and Electromagnetic Interactions of Hadrons

The formulation of analytic $S$-matrix theory has been examined in the absence of time-reversal invariance. As anticipated, no difficulties have been encountered in setting up the necessary formalism: $N{D}^{-1\mathrm{}}$ method, definition of coupling constants, etc. Some successful $S$-matrix calculations have been re-examined without the assumption of $T$ invariance. In all of these, $T$ invariance has emerged as a consequence of the dynamics. Photoproduction of the $N^{*}\mathrm{}\left(1238\right)\mathrm{}$ provides the most interesting example, since $T$ invariance emerges as a consequence of a bootstrap principle. The predicted $T$ invariance implies that several proposed tests for $T$ violation involving the $N^{*}\mathrm{}\left(1238\right)N\gamma$ vertex should yield negative results to the extent that the $S$-matrix theory of this vertex is successful.