# su(2)

1. ### A SU(2) Invariant Lagrangian

Consider two arbitrary scalar multiplets $\Phi$ and $\Psi$ invariant under $SU(2)\times U(1)$. When writing the potential for this model, in addition to the usual terms like $\Phi^\dagger \Phi + (\Phi^\dagger \Phi)^2$, I often see in the literature, less usual terms like: \Phi^\dagger...
2. ### I Why choose traceless matrices as basis?

While writing down the basis for SU(2), physicists often choose traceless hermitian matrices as such, often the Pauli matrices. Why is this? In particular why traceless, and why hermitian?
3. ### I SU(2) invariance implies isotropy?

Hello guys, I've came up with three statements in a discussion with a friend where we were trying to check if we had a clear vision of what isotropy and group invariance would imply in an arbitrary theory of gravity at the level of its matter lagrangian. We got stuck at some point so I came here...
4. ### Insights A Journey to The Manifold SU(2) - Part II - Comments

Greg Bernhardt submitted a new PF Insights post A Journey to The Manifold SU(2) - Part II Continue reading the Original PF Insights Post.
5. ### Insights A Journey to The Manifold - Part I - Comments

fresh_42 submitted a new PF Insights post A Journey to The Manifold - Part I Continue reading the Original PF Insights Post.
6. ### Invariance under SU(2) in quantum mechanics

1. Homework Statement Hi, I'm trying to self-study quantum mechanics, with a special interest for the group-theoretical aspect of it. I found in the internet some lecture notes from Professor Woit that I fouund interesting, so I decided to use them as my guide. Unfortunately I'm now stuck at a...
7. ### I SU(2) representations

Hello! I just started reading about SU(2) (the book is Lie Algebras in Particle Physics by Howard Georgi) and I am confused about something - I attached a screenshot of those parts. So, for what I understood by now, the SU(2) are 2x2 matrices whose generators are Pauli matrices and they act on a...
8. ### A SU(2)_V, SU(2)_A transformations

Within my project thesis I stumbled over the term SU(2)_V, SU(2)_A transformations. Although I know U(1)_V, U(1)_A transformations from the left and right handed quarks( U(1)_V transformations transform left and right handed quarks the same way, while U(1)_A transformations transform them with a...
9. ### SU(2) lepton doublet conjugation rules

I have a left-handed $SU(2)$ lepton doublet: $\ell_L = \begin{pmatrix} \psi_{\nu,L} \\ \psi_{e,L} \end{pmatrix}.$ I want to know its transformation properties under conjugation and similar 'basic' transformations: $\ell^{\dagger}_L, \bar{\ell}_L, \ell^c_L, \bar{\ell}^c_L$ and the general...
10. ### Additional Phase factors in SU(2)

I am curious as to the meaning of, and name given to the phase $\xi(t)$ which may be added as a prefix to the time evolution operator $\hat{U}(t)$. This phase acts to shift the energy of the dynamical phase $<{\psi(t)}|\hat{H}(t)|\psi(t)>$, since it appears in the Hamiltonian along the...