Schwinger Algebra for Quaternionic Quantum Mechanics

TL;DR

This paper extends Schwinger's measurement algebra to quaternionic quantum mechanics, clarifying its properties and constructing quantum fields that relate to known fermion and boson operators in the large particle limit.

Contribution

It introduces a quaternionic generalization of Schwinger's measurement algebra and explores the resulting quantum field theory, connecting it to existing fermion and boson operators.

Findings

Quaternionic measurement algebra generalization

Quantum fields coincide with known fermion/boson operators at large N

Clarification of quaternionic quantum mechanics notions

Abstract

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 $N \to \infty$.