Abstract
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.
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Communicated by A. Jaffe
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Alder, S.L. Quaternionic quantum field theory. Commun.Math. Phys. 104, 611–656 (1986). https://doi.org/10.1007/BF01211069
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DOI: https://doi.org/10.1007/BF01211069