This website, www.CliffordAlgebra.com is about applications of Clifford algebra to QM, specifically to Schwinger's measurement algebra.

In mainstream physics, the elementary particles are described with Pauli spin matrices or Dirac gamma matrices, depending on whether anti particles need to be included. These are matrix representations of Clifford algebras. In order to avoid confusion over representations, we will call these two Clifford algebras the Pauli algebra and the Dirac algebra.

Mathematically, when one moves from the Pauli algebra to the Dirac algebra one adds a "canonical basis vector" to the Clifford algebra. Physically, one increases the number of possible particles that a wave function taking these values could represent. For example, a Pauli algebra spinor might represent either a spin up electron or a spin down electron. A Dirac algebra spinor has twice as many degrees of freedom and can represent any of four cases for the particle, spin up or down electron and spin up or down positron.

We will illustrate the use of the Clifford algebra by expanding the spinors from allowing 4 particles to 8. This will expand the Dirac spinor from just dealing with an electron or neutrino to covering both cases. The purpose for doing this is to define the elementary fermions in a natural manner.

If you want to learn about Clifford Algebra, and particularly the applications of Clifford algebra to particle unification, click the "wiki" button on the left, where you are also invited to post your own contributions and ideas.

Stephen Blake has kindly given me permission to host his beautiful, 280 page LaTex formatted book A. N. Whitehead's Geometric Algebra. This is not Clifford algebra, but it is a close cousin.

As I write this, the website is only a few months old. I have so much more to do here. If you want an email when important additions are made, sign the guestbook.

One of the additions that is already about half completed is a Java based Clifford algebra calculator. By half completed, I mean that I am using one I have written at home, but it is rather difficult for others to get used to, or to modify for their own purposes. With the Dirac algebra, there are 16 complex degrees of freedom (or 32 real degrees), so multiplying two elements of the algebra involves 1024 multiplications and about that many additions. Some hand calculations can get tedious.

This is one of three educational websites that I've recently started, to see more about them, click the "about" button.