Quaternionic wave function

Relativistic Quaternionic Wave Equation II

Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation. Further study of multiparticle systems has us looking into the mathematics of tensor products of Hilbert spaces. The principles of linearity and superpositi...

A Relativistic Quaternionic Wave Equation

We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved quantity which looks like helicity. The principle of superposition is retained in a slightly altered manner. External potentials can be introduced in a way th...

Geometrical Quaternionic Coupling for Three Dimensional Wave Equations

The present work has the scope to show the relationship between four three-dimensional waves. This fact will be made in the form of coupling, using for it the Cauchy-Riemann conditions for quaternionic functions [1], through certain Laplace’s equation in [2]. The coupling will relate those functions that determine the wave as well as their respective propagation speeds. AMS Subject Classificati...

Quaternionic Line-Sets and Quaternionic Kerdock Codes

When n is even, orthogonal spreads in an orthogonal vector space of type O-(2n 2,2) are used to construct line-sets of size (2nm1 + 1)2”-’ in W2”~’ all of whose angles are 90” or cos -1(2-(“-2)/2). These line-sets are then used to obtain quatemionic Kerdock Codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.

On the Zeta Function of Quaternionic Shimura Varieties