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Classification of quantum relativistic orientable objects. (English) Zbl 1217.81150
Summary: Extending our previous work “Field on Poincaré group and quantum description of orientable objects” [D. M. Gitman and A. L. Shelepin, Eur. Phys. J. C, Part. Fields 61, No. 1, 111–139 (2009; Zbl 1189.81089)], we consider here a classification of orientable relativistic quantum objects in $$3+1$$ dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincaré group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.
Reviewer: Reviewer (Berlin)

##### MSC:
 81V25 Other elementary particle theory in quantum theory
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