Quaternionic Dirac equation

Abstract

The quaternionic generalization of the Dirac equation is investigated. From elementary considerations of unitarity and Lorentz invariance it is demonstrated that potentials with quaternionic parts are not consistent with representation independence. This result leads to the conclusion that either quaternionic quantum mechanics singles out a special class of Dirac representations, or that allowed potentials appearing in the problem have no j or k components. If the latter alternative is the case, consideration of nonrelativistic wave mechanics casts doubt on the existence of simple experimental tests of quaternionic quantum mechanics.

Hawking radiation from a dielectric black hole

“…In order to understand the physical mechanism of Hawking radiation, Unruh has proved that in Minkowski spacetime when the quantum field is in a general vacuum state an observer with a straight uniform acceleration will see a thermal state with temperature that is in direct proportion to its internal acceleration T = a/2π , where a is the acceleration of the observer (Unruh 1976;Fulling 1973;Davies 1975). Deser and Levin (1997, 1998, 1999 have provided intrinsic relations between Hawking effect and Unruh effect.…”

A new technique of quaternion equality constrained least squares problem

“…In recent years, applications of quaternion matrices are getting more and more important and extensive in quantum mechanics, rigid mechanics and control theory [1][2][3][4][8][9][10]15,19,[21][22][23][24], it is getting more and more necessary to study the theory and methods of quaternion matrices. In [20], we studied the equality constrained least squares problem of quaternion matrices by means of GSVD and complex representations of quaternion matrices, gave the necessary and sufficient conditions for the quaternion LSE problem to have solutions, and derived a practical algorithm.…”

Split quaternions and particles in (2+1)-space

“…There exist several successful applications of quaternions (see, for example [28][29][30][31]) in formulating of the Dirac equation. For this purpose it is important to define the gradient operator for quaternion-valued functions.…”