Doing Physics witht + x \(i\&^\) + y \(j\&^\)+ z \(k\&^\)quaternions

doug  <sweetser@world.std.com>

Introduction
	A brief history of quaternions
	Multiplying quaternions the easy way
	Inner and outer products
	Understanding a Mathematica notebook

(Overscript[F,  ⇀])   =  
      m (Overscript[a,  ⇀])     Classical Mechanics

F = m a, in an inertial frame, in polar coordinates, and in a rotating 	reference frame
4 tests for a conservative force
The simple harmonic oscillator and wave equation

E  =  γ m (c^2)    Special Relativity

An alternative algebra for boosts 

Problem set questions and solutions from MIT's 8.033, Classical and 	Relativistic Mechanics
PS 1:  Kinematic effects of relativity
PS 2:  More kinematic effects
PS 3:  The Lorentz transformation and the addition of velocities
PS 4:  The Doppler effect, 4-vector invariants, and the twin paradox
PS 5:  Energy, Mass and Momentum
PS 6:  The Compton effect and threshold collision problems

(Overscript[▽,  ⇀])  x (Overscript[B,  ⇀])  
       =  (Overscript[0,  ⇀])     Electricity and Magnetism

The Maxwell equations

Gauge transformations with the Maxwell equations

< φ | ϕ >     Quantum Mechanics

Bracket notation & quaternions: quaternions as a complete inner 	product space
Polar representations
The Klein-Gordon equation
Time reversal

(Overscript[F, ⇀])  =  ((G M m)/(r^2))    Gravity

Gravitational redshift experiments
The length of a quaternion in curved spacetime:  a close relative of 	the affine parameter of general relativity

∴    Conclusions

A (very brief) summary of physics equations written as quaternions
Conclusions