There has been a wide dispersion of approach to the theory of elementary particles that has tended to impede communications and coherent development in this tightly enfolded, cross-disciplinary field, the scene of vigorous recent activity. In the present volume a broad spectrum of mathematicians and physicists is represented: mathematicians concerned with the basically relevant fields; quantum field theorists of the axiomatic and the constructivist persuasions (and some of both); and group-theoretical “single-particles.” But these papers were specifically prepared to give the reader a clear and collected view of all these phases and aspects of development; a reinforcement of method was sought for, not a cancellation of aims.
Moreover, a very high level of mathematical rigor is obtained. It has been noted that in the past decade those theoretical proposals without this virtue have not been able to stand up under scientific scrutiny and critical attack. About half of the text presented here consists of work whose level of rigor is that of contemporary mathematics. The rest, dealing with inherently approximate, intuitive, and heuristic concerns, operates at an equivalent level of scientific precision.
