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...
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?
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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...
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...
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...
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...
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...
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...