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1. ### Prove: SO(3)/SO(2)=S^2

I'm using Rubakov - Classical Theory of Gauge Fields. ##S^2## is the 2-sphere in three-dimensional space. I was thinking - **if** I could prove that each element of SO(3)/SO(2) can be fully characterized by three real parameters such that their moduli sum to 1, then I could set up a one-to-one...
2. ### Prove: SO(3)/SO(2)=S^2

Homework Statement Take the subgroup isomorphic to SO(2) in the group SO(3) to be the group of matrices of the form \begin{pmatrix} g & & 0 \\ & & 0 \\ 0 & 0 & 1 \end{pmatrix}, g\in{}SO(2). Show that there is a one-to-one correspondence between the coset space of SO(3) by this subgroup and...
3. ### Energy of Scalar Field

Ah, that would make a lot of sense (and fix the weird unit problem). Maybe there's a tiny typo in the text.
4. ### Energy of Scalar Field

Homework Statement My question is just about a small mathematical detail, but I'll give some context anyways. (From Rubakov Sec. 2.2) An expression for energy is given by E= \int{}d^3x\frac{\delta{}L}{\delta{}\dot{\phi}(\vec{x})}\dot{\phi}(\vec{x}) - L, where L is the Lagrangian...
5. ### Proving that an alpha particle is a boson

So take two fermions. Together, they can form a particle described by the wave function, ψ: ψ=2^{-0.5}*(ψ_{a}(1)ψ_{b}(2)-ψ_{b}(1)ψ_{a}(2)).. What I need to do is show that this composite particle of two fermions is a boson. I see how this is a simplified version of my original problem, but...
6. ### Proving that an alpha particle is a boson

1. Is there any way to prove that the alpha particle is a boson (its total wave function is symmetric), given that it's made up of two protons (fermions) and two neutrons (fermions)? Homework Equations The total wave function for two identical particles that are (bosons) ψ_tot = 1/√2 * (ψ_a...