compilation of Geometric Algebra and GA physics notes.

[Peeter Joot]

I've collected a set of personal physics-study related GA notes into a
bookish compilation:

http://sites.google.com/site/peeterjoot/math2009/gabook.pdf

... it's a kind of rough concatenation of smaller article size bits, 1-
~10 pages each. Included is some coverage of GA basics, and GA
applications to elementary electromagnetism, special relativity,
Lagrangian play, and Pauli and Dirac matrices.

(be warned that the download is big, ~1000 pages/4Mb).

Peeter

[Lanco]

Hi Peter

It is quite a lot to think over.
Is is mean as a reference book, or do you want some suggestions
regardless of how small they may be?

Lanco

[Peeter Joot]

> Is is mean as a reference book, or do you want some suggestions
> regardless of how small they may be?

Each of the individual bits was written for my own benefit, to either
clarify some topic or to explore it. Even this compilation (I call it
that instead of book due to quality issues) was for my own benefit, so
I can find stuff that I've thought about more easily.

That said, there's enough here that may be of interest to others that
I thought I'd make it accessible. I know it doesn't stand on its own,
it has duplication and reworking of topics that you wouldn't find in a
polished text, has rigor only as much as I felt like at the time, has
an ambiguous target audience (each part written for me and my level of
understanding at the time of writing), has many questions, likely has
many errors, has horrid grammar and spelling, is not structured in a
way that somebody completely new to the subject would find consumable,
has prereqs that are missing, and many other faults especially as a
whole.

However, ... if you are trying to work through a text like
Doran/Lasenby's GA for Physicists, that is quite tough due to brevity
and assumed knowledge (at least for computer-programmer
physicist-wantabee's like me), then there may be parts of this
compilation that has value.

I'm open to any comments, questions, suggestions and feedback, even
for small things. My study is a evenings and weekends activity as I
have time for it, so acting on any comments may not be immediate.

Peeter

[Ginanjar Utama]

Thanks Peeter, I like the Lagrangian and Noether parts.

kind regards,
ginanjar

[Peeter Joot]

> Thanks Peeter, I like the Lagrangian and Noether parts.

There's an interesting GA feature hiding in that section with the rest
of it. Namely, with a multivector Lagrangian density

L = -\epsilon_0 (E + i c B)^2/2 + J.A/c

(ie: both scalar and pseudoscalar grades, instead of just the usual
scalar part including E^2 - c^2 B^2)

When that is varied one arrives directly at Maxwell's equation:

\grad F = J/\epsilon_0 c

instead of having to reassemble it from the tensor equations.

For the macroscopic formulation of Maxwell's equation, it appears one
gets a trivector "current" term along with the regular four vector
current, so I'm curious what grades a multivector Lagrangian for the
macroscopic field equation would have if you can build one (I haven't
yet tried reverse engineering such a Lagrangian from the field
equation).

Peeter