I have no idea what you did!
Move the last term of each equation to the RHS and simply put one equation over the other! The (a_3*a_6) cancel out. Then divide numerator and denominator by (a_1*a_4) and you're done.
Similar for the other equations.
Actually, that's not correct. The arrow on the W boson represents "charge flow". And it is fine to include it, even though it is not a fermion. Indeed, when you have charged bosons, it is useful to include arrows to make sure to distinguish charge and momentum flow in a Feynman diagram (it...
Divide equations 4,6,8 by equations 5,7,9 (you have some typos in those equations, btw):
\frac{\cos{(b_1-b_4)}+r\cos{(b_2-b_5)}}{\sin{(b_1-b_4)}+r\sin{(b_2-b_5)}}=\cot(b_3-b_6),\qquad r=\frac{a_2a_5}{a_1a_4}...
"Vector" means L and R fermions transform the same way:
\psi_L\longrightarrow e^{i\alpha^aT_L^a}\psi_L,\qquad\psi_
R\longrightarrow e^{i\alpha^aT_R^a}\psi_R
Hence + sign.
"Axial" means L and R fermions transform oppositely:
\psi_L\longrightarrow e^{i\alpha^aT_L^a}\psi_L,\qquad\psi_...
Check out this review
http://arxiv.org/pdf/nucl-th/9506035.pdf
and the many references therein. This was where I first started to learn about this stuff.
Actually, my colleague and I are working on a textbook on "Effective Field Theory", but it won't be done for a while. Stay tuned...
The group SU(2)_L x SU(2)_R has 6 generators T^a_L, T^a_R (a=1,2,3).
We can also use generators T^a_L + T^a_R and T^a_L - T^a_R. The first one generates SU(2)_V and the second one generates SU(2)_A. So you can think of vector and axial symmetries as a change of basis of SU(2)^2.
The axial...
Welcome to PF!
That is an excellent analogy: the strong force is described by a theory known as "Quantum Chromodynamics", or QCD, which describes the interactions of quarks with the gluon force carrier. These are the forces that keep quarks bound in nucleons and other similar particles...
That is correct.
That is right. When you build models (or do any kind of "effective field theory", or EFT), the idea is that you have a list of fields and symmetries, and you write down every operator you can that is made of products of the fields and is consistent with those symmetries...
A U(3) matrix has 6 phases and 3 angles. Just write a 3x3 matrix and parametrize each element in terms of a magnitude and a phase and use UU^\dagger=1 - you will find 3 linearly independent relationships between the 9 phases you wrote down in order to make this work. You can always choose an...
radioactive decays (except gamma decays) always change atomic number, so yes, you will have another atom.
I have no idea how to interpret that last paragraph of yours. We spent the last century discovering new particles in experiments. After a lot of research and a lot of money spent, we now...
They are ruled out in most STANDARD scenarios, but dig a little deeper and they can come back! For example, they contribute to "oblique electroweak corrections" (the so called "S parameter" mainly), but if there is a non-standard Higgs boson, then that constraint goes out the window!
The reason N=4 is so important is due to the Maldecena Conjecture, which relates it to a string theory.
Not sure of any review dedicated to N=4 SUSY, but you can take a look at the famous "MAGOO" review (not for the faint-of-heart) that discusses the Maldecena Conjecture. Might be a good place...
proton is not guaranteed to be at any FINITE REGION, is what I meant.
Radioactivity: strong force is strong, it's true, but not always strong enough. If an atom has too many neutrons, the neutrons will want to decay to protons (e.g.: beta decay). If the atom is too large, it will want to...
1. Size of atom is <r>, the quantum expectation value of the radius. There is certainly a probability for the electrons to be "outside" the atom with this definition, but that's not much more than semantics ("size" versus "size" versus "size"). The probability of the electron being "outside"...