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Results tagged with lie-algebra
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user 115846
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.
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Proving gauge transformation of non-abelian field strength
Specifically regarding the derivative. By definition:
$$
U(x) = \exp(i \alpha_a(x) T^{a}) = \sum_{n=0}^{\infty} \frac{(i \alpha_a(x) T^a)^n}{n!}
$$
Taking derivative yields
$$
\partial U = \sum_{n=0} …
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