# Peeter Joot's (OLD) Blog.

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## Refreshed online version of Geometric Algebra book.

Posted by peeterjoot on August 6, 2009

My exploratory physics notes using Geometric Algebra have now been refreshed with the following recent updates:

• July 2, 2009 (ch73) Space time algebra solutions of the Maxwell equation for discrete frequencies
• July 17, 2009 (ch38) Stokes theorem applied to vector and bivector fields
• July 21, 2009 (ch39) Stokes theorem derivation without tensor expansion of the blade
• July 27, 2009 (ch107) Bivector form of quantum angular momentum operator
• July 30, 2009 (ch74) Transverse electric and magnetic fields

These were all first posted in this blog.

The first covers transverse waves in vacuum, and uncovers the solution utilizing a Fourier transform of the Maxwell equation.

The angular momentum article is a factorization of the spatial (or four vector space-time) gradient into $x \wedge \nabla$ and $x \cdot \nabla$ terms.  This factorization is seen in the context of quantum mechanics treating the angular momentum operator in spherical polar coordinates, but only in coordinate form.  I don’t think it is normal to see this outside of quantum mechanics, but there is nothing intrinsically quantum about this projection operation on the gradient or Laplacian operators.  Nothing is done with this result here, and I’d like to revisit this later to play with the implications of this factorization in a classical context.