Group Theoretical Settling of Spin Zero Relativistic Particle Theories

Abstract

In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical methods. Our work has pointed out the necessity of new classes of irreducible representations of the Poincar\'e group the quantum theory of a particle can be based on. For spin 0 particle, four inequivalent theories are completely determined, with fundamental differences with respect to Klein-Gordon theory.