Quaternionic Electron Theory: Dirac's Equation

R. Jagannathan, R. Simon, E. C. G. Sudarshan +1 more

Stefano De Leo, Waldyr A. Rodrigues

We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a nice ``trick'' which allows to avoid the Dirac algebra constraints in formulating our relativistic equation. A brief comparison with other quaternionic formulations is also presented.

Stephen L. Adler

Abstract We turn in this chapter and the next to a discussion of topics relating to relativistic single-particle equations in quaternionic quantum mechanics. In Secs. 11.1 through 11.3 we develop the theory of the quaternionic Klein-Gordon equation, and then proceed in Secs. 11.4 and 11.5 to develop the theory of the quaternionic Dirac equation.

Sergio Giardino

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].