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The possible connection between certain universal symmetry operations and baryon and lepton conservation. Robertson, Dale Alexander

Abstract

The aim of this work is to propose a possible explanation of certain conservation laws which hold in the reactions among elementary particles. The laws in question are those of conservation of baryon number and conservation of lepton numbers. These are additive quantum numbers which take the values +1, -1, or 0, for single particles. At the present time, these laws must be considered as empirical conservation laws, whose origin is not known. Certain universal symmetry operations must be represented by anti-unitary operators whose square is -1. The existence of such an operator leads to a super-selection rule. The Hilbert space is decomposed into two orthogonal subspaces, with no observables having matrix elements connecting the two subspaces. In the presence of a super-selection rule, an operator can be constructed, which is an observable whose eigenvalues are conserved, and whose eigenvalues have the properties of an additive quantum number. One has one such operator for the baryons, and two for the leptons. A consistent classification of the elementary particles is worked out, which allows the conservation laws to be explained as a result of super-selection rules, provided that the masses of the particles have suitable transformation properties.

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