Single-Particle Electrodynamics - Assassination Science

A.3.17
Orders
For the purposes of this thesis, the terminology surrounding the term order
is defined as follows:
A term T is said to be “of order f(A)”, where f(A) is some function f of
some quantity A, if, were T to have its (implicit or explicit) dependencies on
A written out explicitly, the resulting explicitly-written term would, when
simplified, contain a factor of f(A), and no other dependency on A.
If the function f(A) is a power A n of A, then T may be simply said to be
“of order n in A”. The power n may, in general, be of arbitrary type, but in
practice it is usually integral.
If unambiguous, the term T may be simply said to be “of order n”,
without explicitly mentioning A, if the preceding context makes it clear that
it is the order of A that is being discussed.
An expression E is said to be “of order n” in some quantity A if the
lowest (highest) order in A of any of its terms is n; the choice of whether it
is the lowest or highest order depends on the application.
An expression E is said to be “expanded to order n in A” if all of the
terms in E with order in A less than (greater than) or equal to n are written
out explicitly, and the remaining terms—if any—replaced with the symbol
+ O(A m ), (A.20)
where m is the lowest (highest) order in A of the omitted terms. If E contains
no terms of higher (lower) order in A than n, then the symbol +O(A m ) shall
not be used.
A.3.18
Covariance
Consider the “G” group, where “G” stands for the name of the person or
other object that the group is named after. Any arbitrary mathematical
quantity that transforms as a representation of the G group is referred to
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