Brian Granger wrote:
You might want to look at the geometric algebra module in sympy and chapters
8 and 9 of
"Geometric Algebra for Physicists" by Doran and Lasenby for how you map the
bra-ket algebra
onto geometric algebra.
Thanks for the link. For reletivistic QM this could be useful.
Cheers,
Brian
For non-relativistic QM the basis vectors of the Geometric Algebra of
3-dimensions have the same commutation relations as the Pauli matrices.
If the three dimensional basis vectors are sigma_1, sigma_2, and sigma_3
with pseudo scalar
I = sigma_1*sigma_2*sigma_3 (geometric product) then the mapping of the
pauli spinor, |psi>, to the even multivector psi is
[ a^0+i*a^3]
|psi> = [ ] <---> psi = a^0+a^k*I*sigma_k
(implied summation k = 1 to 3, a's all real)
[-a^2+i*a^1]
This is equation 8.20 in Doran and Lasenby. In chapter 9
non-relativistic two particle states are covered as an example for
general n-particle states.
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