Single-Particle Electrodynamics - Assassination Science

Section B.2: The electromagnetic field
The definition of the electromagnetic field strength tensor F (x) in terms of
the four-potential A(x) is given. The Maxwell equations are listed in various
forms. The dual field strength tensor ˜F (x) is defined. Explicit components
are listed for F and ˜F .
Various quadratic identities involving products of F and ˜F , that are not
commonly known, are listed.
Section B.3: Three-vectors
Various identities are listed for three-vector operations. These are a copy of
those given in the front cover of Jackson [113], and are listed here only for
convenience.
Section B.4: Alternating functions
The connection between the three- and four-dimensional alternating functions,
according to the sign convention established in Section A.5.4, is listed.
The contractions of two four-dimensional alternating functions over one, two,
three and four indices are given explicitly.
Section B.5: Four-vector cross-product
Explicit components for the four-vector cross-product operation, defined in
Section A.8.10, are given. Cyclic invariance of the four-cross-product is illustrated.
Section B.6: Radiation reaction gradients
Various explicit expressions are given for the gradients of field expressions in
some given direction. These are used for the gradient-force radiation reaction
calculations in Chapter 6.
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