Nearly Periodic Matrix Operators For Physics

About the Book

            The first seven chapters of the book build a case of the validity of certain matrix operators in theoretical physics. A simple, generalized Lorentz transformation, that yields correct results in every case and leads to a generalized relativistic velocity vector addition rule, was discovered. The addition rule leads, in its turn, to an electron spin model with the correct gyromagnetic ratio.

            A differential matrix, D*₁, when multiplied into the electromagnetic vector potential, yields the electromagnetic fields, iE +B . The complex conjugate, D₁, operating on these same fields gives the complete set of Maxwell’s equations in  essentially one step. Operation again with D*₁ on the Maxwell equations or on the charge-current density 4-vector yields the charge-current density conservation law in 4 dimensional form, and so on. Finally, the tour de force of electromagnetism is completed by the surprising result that arbitrary motion of a charge automatically produces E-M fields with zero time components.

            Operation of the D*₁ matrix on the energy-momentum vector yields the Schroedinger operators for energy and momentum. The dot product of the Lorentz transformed position vector of a particle with a suitable propagation vector yields an argument for a wavefunction that can be localized or not localized to any reasonable degree and has both explicit group and phase velocities, a purely oscillatory part, and a spin part.

            Other results are as follows: Dirac matrices are found  to be nearly periodic matrices also. Derivations of two of Hamilton’s canonical equations are obtained by operation with a D matrix, constructed from derivatives with respect to the generalized coordinates or the canonical momenta, on the energy-momentum vector.

            Finally, a surprising result, which is not yet completely substantiated and bears on the effects of gravitational forces, appears. It may be that space curvature is not necessary for gravitation.

About the Author

This is my first book. Other publications include about a dozen scientific and engineering papers. PhD in Physics with honors from University of Texas at Austin, 1972. BS in physics with honors from University of Texas at Austin, 1955. Phi Beta Kappa, Sigma Pi Sigma, Phi Kappa Phi, Zwettler Bierbruderschaft.