Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with lie-algebra
Search options questions only
not deleted
user 263243
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.
2
votes
2
answers
578
views
How do I show that a tensor product representation of $L(SU(2))\equiv su(2)$ is reducible?
So I have been reading about the irreducible representations of the Lie algebra $L(SU(2))$ and came across the Cartan-Weyl basis:
$$ H = \sigma_3 $$
$$ E_+ = \frac{1}{2}(\sigma_1+i \sigma_2) $$
$$ E_ …
- 4,064
4
votes
0
answers
225
views
Why is $\mathfrak{so}(3,1)_{\mathbb{C}}^\uparrow \cong \mathfrak{su}_\mathbb{C}(2) \oplus \m... [duplicate]
I am studying the orthochronous Lorentz algebra $\mathfrak{so}(3,1)^\uparrow $ and it reads
$$ [X_i,X_j]=i \varepsilon_{ijk} X_k $$
$$ [X_i,Y_j]=i \varepsilon_{ijk} Y_k $$
$$ [Y_i,Y_j]=-i\varepsilon_ …
- 4,064
1
vote
1
answer
532
views
What is the trace in the Chern-Simons action
I have been looking at the Chern-Simons Lagrangian in $(2+1)$-dimensional spacetime $M$ in terms of a gauge field $A$:
$$ S[A] = \frac{k}{4 \pi}\int_M \text{Tr}(A \wedge \text{d}A+ \frac{2}{3}A \wedg …
- 4,064
26
votes
4
answers
1k
views
How does complexifying a Lie algebra $\mathfrak{g}$ to $\mathfrak{g}_\mathbb{C}$ help me dis...
I have been studying a course on Lie algebras in particle physics and I could never understand how complexifying helps us understand the original Lie algebra.
For example, consider $\mathfrak{su}(2) …
- 4,064