Peeter’s Notes: new version posted of gabook.pdf and first post of miscphyiscs.pdf
Posted by peeterjoot on November 11, 2009
NOTE: The version referred to below is now old. See for updated release notes, and a link to the new latest version.
I’ve now posted a new revision of my collection of Geometric Algebra related physics notes. If I kept track of what was in the last version properly, new content is listed below.
Also posted in its entirety is the remainder of my miscellaneous non-GA physics notes. Have some worked problems on QM and a few other misc bits that could possibly be of interest to a physics student. These non-GA notes should generally be more accessible than the gabook.pdf content since only standard mathematical tools are required for most of it.
• Aug 6, 2009 Comparing phasor and geometric transverse solutions to the Maxwell equation Attempting to use the pseudoscalar as the imaginary in a wave equation phasor expression leads to specific results. Examine these and contrast to scalar imaginary phasors.
• Aug 10, 2009 Covariant Maxwell equation in media Formulate the Maxwell equation in media (from Jackson) without an explicit spacetime split.
• Aug 14, 2009 (INCOMPLETE) Geometry of Maxwell radiation solutions After having some trouble with pseudoscalar phasor representations of the wave equation, step back and examine the geometry that these require. Find that the use of I ˆz for the imaginary means that only transverse solutions can be encoded.
• Aug 16, 2009 Graphical representation of Spherical Harmonics for l = 1 Observations that the first set of spherical harmonic associated Legendre eigenfunctions have a natural representation as projections from rotated spherical polar rotation points.
• Aug 31, 2009 Generator of rotations in arbitrary dimensions. Similar to the exponential translation operator, the exponential operator that generates rotations is derived. Geometric Algebra is used (with an attempt to make this somewhat understandable without a lot of GA background). Explicit coordinate expansion is also covered, as well as a comparison to how the same derivation technique could be done with matrix only methods. The results obtained apply to Euclidean and other metrics and also to all dimensions, both 2D and greater or equal to 3D (unlike the cross product form).
• Sept 4, 2009 Translation and rotation Noether field currents.
• Sept 6, 2009 Bivector grades of the squared angular momentum operator.
• Sept 13, 2009 Relativistic classical proton electron interaction.
• Sept 20, 2009 Spherical Polar unit vectors in exponential form.
• Sept 22, 2009 Lorentz force from Lagrangian (non-covariant)
• Sept 24, 2009 Electromagnetic Gauge invariance.
• Oct 27, 2009 Spherical polar pendulum for one and multiple masses, and multivector Euler-Lagrange formulation.
• Nov 4, 2009 Spherical polar pendulum for one and multiple masses (Take II)