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...
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...
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...
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...
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...