Su(2) Definition and 121 Threads

For SU(2) rotational invariance there is a clear interpretation of what all the generators mean. They correspond to operators whose eigenvalues are some observable. The noether charges correspond to the x,y and z components of angular momentum. The casimir is just the total angular momentum...

I'm having a memory blank on this particular area of field theory. Is the product of two spinors a scalar or scalar type entity and if so, can I treat it like a scalar? (i.e. move it around without worrying about order etc) i.e. is \Phi_1^{\dagger} \Phi_1 a scalar? and if so does...

I'm trying to understand this paper which the author claimed that he had constructed an infinite dimensional representation of the su(2) algebra. The hermitian generators are given by J_x=\frac{i}{2}(\sqrt{N+1}a-a^\dagger\sqrt{N+1} ) J_y=-\frac{i}{2}(\sqrt{N+1}a+a^\dagger\sqrt{N+1} )...

I wanted to ask if there is any connection between the SU(2) group for the spin 1/2 and the gauge group of weak interactions. I feel there isn't much of a connection other than the fact that they share the same group properties, but I am not sure. Thanks to anyone in advance that can clarify...

I'm studying Lie groups using G. 't Hooft's tutorial: http://www.phys.uu.nl/~thooft/lectures/lieg.html In page 34, he introduces superscript and subscript indices starting from equation 6.27: \phi_{\alpha} \rightarrow \phi_{\alpha}' = X_{\beta}^{\alpha}\phi^{\beta} What is the...

hi ,i see from a book su(2) has the form U\left(\hat{n},\omega\right)=1cos\frac{\omega}{2}-i\sigmasin\frac{\omega}{2} in getting the relation with so(3),why we choose \frac{\omega}{2},how about changing for \omega? thank you

Hi there! Doesn't seem like a hard problem.. Homework Statement Show that the 3 isospin operators, defined by T_{+}\left\vert p\right\rangle =0, T_{-}\left\vert n\right\rangle =0, T_{+}\left\vert n\right\rangle =\left\vert p\right\rangle, T_{-}\left\vert p\right\rangle =\left\vert...

there's a surjective homomorphism from a : SU(2) --> SO(3) The kernel of this homomorphism is the center of SU(2) which is Z/2Z. Now the fundamental group of SO(3) is Z/2Z. This is a general thing. The simplest version of my question is how is the center of SU(2) related to the...

SU(2) and SO(3) "have the same Lie algebra". While I understand that their corresponding lie algebras su(3) and so(2) have the same commutator relations \mbox{SO(3)}: \left[ \tau^i, \tau^j\right] = \iota \varepsilon_{ijk} \tau^k \mbox{SU(2)}: \left[ \frac{\sigma^i}{2}...

I've read that the choice of Gauge group \mathrm{SU}(2)_\mathrm{L}\times \mathrm{U}(1)_\mathrm{Y} can be justified by the fact that the electromagnetic charge and the flavour-changing weak charge do not form a closed SU(2) current algebra. The solution is to tack on an additional U(1) group and...

I'm taking a course on Lie groups and am reading alongisde Cahn's semi-simple lie algebras and their representations. On page 4 he starts to construct a representation T of the Lie group corresponding to SU(2) acting on a linear space V, by defining the action of T_z and T_+ on a vector v_j...

Any rotation about n(θ, φ) in SU(2) can be represent as u(n, ω) = I cos[ω/2] - i(σ.n)sin[ω/2],where I is the unit matrix and i is the complex number.Right? But can someone tell me why ω/2 rather than ω? Waiting for your response.Thank you.

Homework Statement I'm trying to understand why particles have both spin and angular momentum in terms of group theory. As I understand it orbital angular momentum comes from the normal generators SO(3) which are intuitively infintesimal rotations so d/d(theta) etc. Also spin comes from...

I’ve got a couple of conceptual questions on spin etc, and any help would be appreciated. First of all reading books (eg. Sakuri) it seems like authors tend to show there’s a homomorphism between the groups SO(3) and SU(2) using Euler angles etc. I know the Pauli matricies act as generators...

Sorry if this is a silly question (I'm doing a fairly basic QM course but am doing a bit of extra reading for interest etc.), but why for an spin hbar/2 particle is the spin operators (the Pauli matricies) the generator of su(2)? I understand why generally generators act as conserved...

Hi. I am having trouble proving that the irreducible representations of SU(2) are equivalent to their dual representations. The reps I am looking at are the spaces of homogenous polynomials in 2 complex variables of degree 2j (where j is 0, 1/2, 1,...). If f is such a polynomial the action of...

Hi. I'm a relative layman with a CS/Math background (with more of the former than the latter) and I've been trying to follow some of the recent developments in physics with a hope of eventually understanding at least the outline of the underlying math. I had a couple of questions about some...

I'm trying to learn some theory of inflation, and recently read a paper by Andrei Linde from 1982 where he suggested a scenario where inflation is driven by the phase transition SU(5) -> SU(3) x SU(2) x U(1). Now SU(5) is known to not be a good candidate as an extension of the standard model...

Does anybody know whether the following irreducible representations of SU(2) are unitary? g belongs to SU(2) [U_j(g) f](v) = f(g^{-1} v) f is an order-2j homogeneous complex polynomial of two complex variables v = (x, y) e.g. for j = 1, f = 2x^2 + 3xy + 4y^2

Complexifying su(2) to get sl(2,C)---group thread footnote On the group thread midterm exam (which we never had to take!) it says what is the LA of the matrix group SL(2, C) and the answer is the TRACE ZERO 2x2 matrices. So that is what sl(2,C) is. When you exponentiate one of the little...

Let φ SU(2) ---> SO(3) be the double covering Any irreducible representation of SO(3) pulls back by φ to provide an irreducible representation of SU(2) on the same finite dimensional Hilbert space. this seems clear, almost not worth saying: the pullback is obviously irred. and...