Abstract
The class of representations of the Poincare group for the formulation of relativistic quantum theories of single particle is consistently extended. In so doing new species of such representations are singled out. By making use of the enlarged class quantum theories of Klein-Gordon free particle are formulated without the problems suffered by the early theory. Furthermore, new species of consistent theories can be developed.
Highlights
The identification of the irreducible representations of the Poincare group P lays the groundwork for the formulation of the relativistic quantum theories of one elementary free particle
One of the classes discarded is that of the irreducible representations with anti-unitary space inversion operator [2], [3], [4]; quantum theories of a particle characterized by anti-unitary space inversion operator can be consistently developed [5], but even anti-unitary space inversion operators turn out to be indispensable for formulating complete quantum theories of Klein-Gordon particles without the inconsistencies that plagued the early theory [6]
In order to ascertain that our work is not meaningless from a theoretical physics point of view, in the final section 6 we show that consistent relativistic quantum theories of a particle can be formulated, which are based on irreducible representations singled out by the present work and not considered in the literature
Summary
The identification of the irreducible representations of the Poincare group P lays the groundwork for the formulation of the relativistic quantum theories of one elementary free particle. One of the classes discarded is that of the irreducible representations with anti-unitary space inversion operator [2], [3], [4]; quantum theories of a particle characterized by anti-unitary space inversion operator can be consistently developed [5], but even anti-unitary space inversion operators turn out to be indispensable for formulating complete quantum theories of Klein-Gordon particles without the inconsistencies that plagued the early theory [6] These arguments point out that the following tasks should be accomplished in order to effectively identify the possible quantum theories of a free particle.
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