the link between the sachs and o(3) theories of electrodynamics
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THE LINK BETWEEN THE SACHS AND O(3) THEORIES OF ELECTRODYNAMICS M. W. EVANS CONTENTS I. Introduction I I . The Non-Abelian Structure of the Field Tensor III. The Covariant Derivative IV. Energy from the Vacuum V. The Curvature Tensor VI. Generally Variant 4-Vectors VII. Sachs Theory in the Form of a Gauge Theory VIII. Antigravity Effects in the SachsTheory IX. Some Notes on Quaternion-Valued Metrics Acknowledgments References
I. INTRODUCTION In this volume, Sachs [I] has demonstrated, using irreducible representations of the Einstein group, that the electromagnetic field can propagate only in curved spacetime, implying that the electromagnetic field tensor can exist only when there is a nonvanishing curvature tensor K,,“. Using this theory, Sachs has shown that the structure of electromagnetic theory is in general non-Abelian. This is the same overall conclusion as reached in O(3) electrodynamics [2], developed in the second chapter of this volume. In this short review, the features common to Sachs and O(3) electrodynamics are developed. The B”’ field of O(3) electrodynamics is extracted from the quatemion-valued LP”’ equivalent in the Sachs theory; the most general form of the vector potential is considered in both theories, the covariant derivatives are compared in both theories, and the possibility of extracting energy from the vacuum is considered in both theories.
Modern Nonlinear Optics, Pun 2. Second Edition, Advances in Chemicul Physics, Volume 119, Edited by Myron W. Evans. Series Editors I. Prigogine and Stuart A. Rice. ISBN O-471-38931-5 I
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