Quaternionic Formulation of Dirac Theory in Special and General Relativity

Quaternionic Formulation of Dirac Equation

ABSTRACT : Quaternion Dirac equation has been obtained from the square root of Klein-Gordon equation in compact and consistent way. Dirac matrices are described as quaternion valued and the Dirac Hamiltonian is considered as Hermitian with real eigenvalues of energy. Dirac spinors and free particle energy solution has been obtained in terms of one component, two-component and four-component Dir...

General Relativity in terms of Dirac Eigenvalues

The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of “observables” for general relativity. Recent work of Chamseddine and Connes suggests that they can be taken as variables for an invariant description of the gravitational field’s dynamics. We compute the Poisson brackets of these eigenvalues and find t...

Lagrangian Formulation of General Relativity

Hyperbolic Formulation of General Relativity

Einstein’s theory, viewed mathematically as a system of second-order partial differential equations for the metric, is not a hyperbolic system without modification and is not manifestly well-posed, though physical information propagates at the speed of light. A well-posed hyperbolic system admits unique solutions which depend continuously on the initial data and seems to be required for robust,...

The Special Theory of Relativity