Irreducible representations electrodynamics

Invariance principle, 664 Invariance properties of quantum electrodynamics, 664 Inventory problem, 252,281,286 Inverse collisions, 11 direct and, 12 Inverse operator, 688 Investment problem, 286 Irreducible representations of crystallographic point groups, 726 Isoperimetric problems, 305 Iteration for the inverse, 60... 

In Eq. (5), the product q q is quaternion-valued and non-commutative, but not antisymmetric in the indices p and v. The B<3> held and structure of 0(3) electrodynamics must be found from a special case of Eq. (5) showing that 0(3) electrodynamics is a Yang-Mills theory and also a theory of general relativity [1]. The important conclusion reached is that Yang-Mills theories can be derived from the irreducible representations of the Einstein group. This result is consistent with the fact that all theories of physics must be theories of general relativity in principle. From Eq. (1), it is possible to write four-valued, generally covariant, components such as... 

To this list can now be added the advantages of 0(3) over U(l) electrodynamics, advantages that are described in the review by Evans in Part 2 of this three-volume set and by Evans, Jeffers, and Vigier in Part 3. In summary, by interlocking the Sachs and 0(3) theories, it becomes apparent that the advantages of 0(3) over U(l) are symptomatic of the fact that the electromagnetic field vanishes in flat spacetime (special relativity), if the irreducible representations of the Einstein group are used. 

Technical Appendix B 0(3) Electrodynamics from the Irreducible Representations of the Einstein Group References... 

TECHNICAL APPENDIX B 0(3) ELECTRODYNAMICS FROM THE IRREDUCIBLE REPRESENTATIONS OF THE EINSTEIN GROUP... 

It can therefore be inferred that 0(3) electrodynamics is a theory of Rieman-nian curved spacetime, as is the homomorphic SU(2) theory of Barrett [50], Both 0(3) and SU(2) electrodynamics are substructures of general relativity as represented by the irreducible representations of the Einstein group, a continuous Lie group [117]. The Ba> field in vector notation is defined in curved spacetime by... 

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