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Quaternionic quantum field theory. (English) Zbl 0594.58059
Author’s summary: ”We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation. The theory takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.”
Reviewer: N.Jacob

MSC:
58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
35Q99 Partial differential equations of mathematical physics and other areas of application
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
15A66 Clifford algebras, spinors
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