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Results tagged with lie-algebra
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user 3597
A vector space $\mathfrak{g}$ over some field $F$ and kitted with a bilinear, antisymmetric and Jacobi-identity-fulfilling product ("Lie Bracket" or "commutator"). In physics, most often arises as the Lie algebra (tangent space to the identity) of a Lie group; in gauge theories, basis vectors of the gauge group's Lie algebra correspond to Noether currents and conserved quantities.
7
votes
1
answer
633
views
Coupling Coefficients in SO(4)
I have two equations (from two distinct authors) for the decomposition of a coupling coefficient of SO(4) (i.e. Wigner 3j-symbol for SO(4)). In the first:
\begin{equation}
\left(
\begin{array}{ccc}
…
- 819
3
votes
1
answer
3k
views
General procedure for Clebsch-Gordan expansions
I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps …
- 819
16
votes
1
answer
677
views
How to evaluate this sum of coupling coefficients?
I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form:
$$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ \beg …
- 819