Schwinger Algebra for Quaternionic Quantum Mechanics

Details Schwinger Algebra for Quaternionic Quantum Mechanics Schwinger Algebra for Quaternionic Quantum Mechanics

1997-02-10

arxiv.org/abs/hep-th/9702080v1

Found.Phys. 27 (1997) 1011-1034

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, Plain TeX

Scientific paper

10.1007/BF02551150

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.

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