summary.txt

This is a quick overview of the eight files you will find in this archive.

Thanks for downloading! Feel free to email me at jem497@cornell.edu if you
have any questions or suggestions for this computation.

## E&M_computation_main.m ##

Imports all the rest, then performs the computations described in the derivation
section of the paper "Radiation reaction on a small charged body to second
order". This involves using the retarded self field and the equations of motion
to derive a cascaded ruleset and ultimately arrive to a set of perturbative
equations of motion for the worldline, mass, and spin of a small charged body.

## 3+1Utils.m ##

This is a separate package for dealing with many of the general troubles I ran
across when trying to perform a 3+1 split in xTensor.  The rough idea is that we
want to be able to define a separate tangent space for the 4-index and the
3-index, then associate them in a meaningful way. Many of the utilities have to
do with dealing carefully with derivatives, and there is a separate construction
for the family of tensors, the kronecker deltas.


## Retarded3+1Coords.m ##

A specific rules family for the retarded coordinates, documented well in Eric
Poisson's Living reviews of relativity. This relies on the 3+1 split I construct
in the previous part, and in particular, makes liberal use of kronecker deltas
between the retarded coordinates and the 'frame' coordinates which carry an
implicit contraction with the fermi-transported tetrad. Of particular interest
are RetCanon and BasisCanon utility functions, which are canonicalization
utilities. RetCanon will both canonicalize and substitute the retarded basis and
metric values, BasisCanon will not substitute but will organized the kronecker
deltas. BasisCanon has support for arguments to make it more safe for partial
derivatives and/or subexpressions.

## NullIntegration.m ##

This carries the definition and utilities for integration along future null
surfaces, and the 2-dimensional spherical boundary of a future null
surface. This is performed often in the derivation, so utilities for
appropriately commuting invariant tensors through the integrals and performing
integration by parts are included.

## sumrules.m ##

This contains a brief definition of a critical utility that I've created - the
sumrules. This allows a sum of terms to be extracted from a long expression
which has Plus as the head without the standard mathematica pattern-matching
combinatoric time scaling. Instead, this performs a linear search using
MatchQ. The overhead is large for short expressions, but for expressions of at
least ~10 terms, I've found the linear scaling takes over and sumrules performs
far better than the mathematica native.

## EnMTensors.m ##

Direct definitions and rules for the electromagnetic tensors used in this
computation. Included also is a custum perturbation code that is a slimmed-down
version of the xTensor perturbation evaluates more quickly. There is also a
'Qerturb', a second index of perturbation, which is used in the code to
represent an expansion in inverse-r most typically.

## selfField.m ##

This includes the computation of the retarded and advanced self fields to the
order which they are required for the self-force computation.  In the current
release, this still performs these computations on the fly, so the import step
for this piece of the code is comparatively long.  This also generates the field
strength tensor associated with the retarded field, and the regular (half
retarded minus half advanced) field strength, and the stress energy tensor of
the retarded-retarded piece.

## EnMRuleGeneration ##

This contains utilites for generating the cascaded rule sets that are necessary
in the perturbative step of the computation. It includes both rule generation
utilities for sumrules and standard single-term replacements (for which
mathematica native matching works fine), as well as the heuristics for choosing
the best term or set of terms to be placed on the 'left hand side' of those
equations for this specific E&M computation.