Single-Particle Electrodynamics - Assassination Science

where the first product is of course an outer-product (simple multiplication).
Parentheses or brackets must be used around proper-time derivatives of
kinematical quantities where there is a difference between the partial and
covariant derivatives (see Section A.8.22).
A.8.8
Chained dot-product rings
If a central dot both precedes and follows a product of one or more nondereferenced
four-tensors, an inner-product over the first index of the leftmost
tensor and the second index of the rightmost tensor is deemed to take place;
for example, if F , G and H are four-tensors, then
·F · ≡ F α α, (A.49)
·F ·G· ≡ F α βG β α, (A.50)
·F ·G·H· ≡ F α βG β γH γ α. (A.51)
The notation is meant to imply that the factors are conceptually wrapped
into a ring, whereby the leading and trailing central dots would be merged
into one.
A.8.9
Epsilon products
If A, B, C and D are four-vectors, then the epsilon product of them is defined
as
ε(A, B, C, D) ≡ ε αβµν A α B β C µ D ν .
(A.52)
If one entry in the ε( ) symbol is a four-tensor, and there are only two commas
in the symbol, then the four-tensor is deemed to carry the two adjacent
indices in the inner-product. Likewise, if there are two four-tensor entries in
the ε( ) symbol, and only one comma, then the two four-tensors are deemed
to carry the four indices. For example, if A and B are four-vectors, and F
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