The Many Faces of Maxwell, Dirac and Einstein Equations

A Clifford Bundle Approach
1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-3-642-09038-7
Verlag: Springer

Buch, Englisch, Band 722, 445 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 692 g

Reihe: Lecture Notes in Physics

Maxwell, Dirac and Einstein’s equations are certainly among the most imp- tant equations of XXth century Physics and it is our intention in this book to 1 investigate some of the many faces of these equations and their relationship and to discuss some foundational issues involving some of the theories where they appear. To do that, let us brie?y recall some facts. Maxwell equations which date back to the XIXth century encodes all cl- sical electromagnetism, i. e. they describe the electromagnetic ?elds generated by charge distributions in arbitrary motion. Of course, when Maxwell f- mulated his theory the arena where physical phenomena were supposed to occur was a Newtonian spacetime, a structure containing a manifold which is 3 di?eomorphic to R×R, the ?rst factor describing Newtonian absolute time 2 [25] and the second factor the Euclidean space of our immediate perception. In his original approach Maxwell presented his equations as a system of eight linear ?rstorderpartialdi?erentialequations involvingthe components of the electricandmagnetic?elds[17]generatedbychargeandcurrentsdistributions 3 with prescribed motions in vacuum. It was only after Heaviside [12], Hertz and Gibbs that those equations were presented using vector calculus, which by the way, is the form they appear until today in elementary textbooks on Electrodynamics and Engineering Sciences. In the vector calculus formalism Maxwell equations are encoded in four equations involving the well known divergentandrotationaloperators.

Zielgruppe

Research

Autoren/Hrsg.

Rodrigues, Waldyr A.

Oliveira, Edmundo C.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

Multiform and Extensor Calculus.- The Hidden Geometrical Nature of Spinors.- Some Differential Geometry.- Some Issues in Relativistic Spacetime Theories.- Clifford and Dirac-Hestenes Spinor Fields.- Lagrangian Formalism in Minkowski Spacetime.- Conservation Laws on Riemann-Cartan and Lorentzian Spacetimes.- The DHE on a RCST and the Meaning of Active Local Lorentz Invariance.- Gravitational Theory in Minkowski Spacetime.- On the Many Faces of Einstein’s Equations.- Maxwell, Dirac and Seiberg-Witten Equations.- Superparticles and Superfields.