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# Questions tagged [lie-algebra]

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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### How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
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### Bosonic commutation relations for force carriers?

Why are force carriers bosons? The easiest answer that I can give myself is that the gauge field $A_\mu$ is introduced like this: $$\partial_\mu \rightarrow D_\mu = \partial_\mu+ieA_\mu,$$ so it ...
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### Kac-Moody algebra from WZW model via Poisson brackets

In 'Non-abelian Bosonization in Two Dimensions', Witten shows that the Poisson brackets of the currents that generate the $G\times G$ symmetry of the WZW model give rise to a Kac-Moody algebra upon ...
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### What's the difference between a generating function and a generator?

Usually in physics we use the notion generator to describe the infinitesimal elements associated with any finite Lie group transformation. But in the context of the Hamiltonian formalism, all authors ...
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### Products of Lie-Groups versus Lie-Group Extensions in Physics

The Standard Model of elementary particle physics is a gauge theory based on the Lie group $U(1) \times SU(2) \times SU(3)$. From the mathematical perspective I read that: Simple Lie groups have ...
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### Isospin of pions

Suppose that I have two pions with zero relative angular momentum. I want to find possible total isospin values. What I'm thinking is that their state should be symmetric since they are bosons. Each ...