I am looking for some notes/reviews on confinement and Higgs phases suitable for Fermionic/Bosonic matter coupled to Abelian ($Z_2$ or $U(1)$ etc) gauge fields.
The purpose is to understand issues related to strongly interacting spin systems in 1,2,3 spatial dimensions, associated phase transiti...
@obe : what do you want to know? If you're not sure, read about the Einstein-de Haas effect and about Goudsmit and the discovery of electron spin: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates".
@obe : good stuff. meanwhile don't think spin is something magical. Take a look at an old version of the Wikipedia Stern–Gerlach article. It contains a non-sequitur that says the electron can't be rotating like a planet, so it can't be rotating at all. That's wrong. Of course it isn't rotating like a planet, it's a spin ½ particle. Duh!
@0celo7 : Follow my links, read the Goudsmit article. There is an actual rotation going on. That's why the electron has a magnetic moment. The Einstein-de Haas effect "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". The word spin is correct.
@Huy it's...different. I have to hold the mouse differently than I did my old one and I've been killed in BF4 because I didn't have my thumb in the proper place
Can someone tell me the significance of these badges:
Precognitive : Followed the Area 51 proposal for this site before it entered the commitment phase
Beta : Voted 10 times, added 3 posts score > 0, and visited the site on 3 separate days during the private beta
My questions:
What...
I'm going mad about the problem.
I really don't understand why do electron have 1/2 spin number, why they are not actually spinning.
I can accept that the electrons have their own magnetic field, which is certain, but why do they have $\hbar\sqrt3/2$ of angular momentum, and I don't know what t...
@dmckee : spin is real. And I quote: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates".
The evidence says electron spin is real. The Einstein-de Haas effect is real. So is electron magnetic moment. And electrons and positrons don't move the way they do for fun.
@JohnDuffield For the nth time: the Einstein-de Haas effect says that spin is angular momentum (which no one has argued about for more than 50 years). It doesn't say that is is $\mathbf{r} \times \mathbf{p}$.
@Danu I think you are right, it is standard and obvious, and also contrary to what I think, attractors and repellers can demonstrate more complex behaviour than my surface analogy can handle
@0celo7 : that the electron can't be spinning like a planet so it can't be spinning at all. See the old Stern-Gerlach article: "Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values measured along any axis, +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates
then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 2.8 fm (the classical electron radius), its surface would have to be rotating at 2.3×10^11 m/s. The speed of rotation at the surface would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible.[2] Instead, the spin angular momentum is a purely quantum mechanical phenomenon."
@0celo: spin ½ rotation. See the Dirac spinor article on Wikipedia. Note the reference to bispinor. Think of a biaxial rotation. Where the rotates goes round a major axis AND round a minor axis. Think of the AND as a multiplier. Hence round and round.
@JohnDuffield There is no such thing as a "spin 1/2 rotation". Objects behaving as spin-1/2 objects are not transforming in a proper representation of the rotation group, and the spaces on which half-integer spins act are necessarily complex, not real.
@0celo7 : I'll explain it once you've got your calculator out and worked out the value. You know that if you see a 4π it's something to do with a sphere, don't you? And you've heard of spherical harmonics, haven't you?
@ACuriousMind : yes, it is an actual rotation. The electron and the positron don't move the way that they do in a magnetic field for fun. Or because of the Lorentz force. They do so because they're "spinors", with the opposite chirality.
@ACuriousMind : the Lorentz force is just an expression that describes how they move helically when you chuck 'em through a solenoid. To understand why they move helically, you have to appreciate that spin is real. It isn't something that surpasseth all human understanding.
@0celo7 : get you calculator out. You'll see what's so special about it.
@ACuriousMind : yes, the Lorentz force is because they have spin. There is no magical mysterious action-at-a-distance force doing it. The electron follows a curved path because spin is a real rotation. As for me showing it, have a look at this curl article.
@Danu I've never seen that 'projecting from a complex to a holomorphic tangent space' thing, looks like witchcraft to me but I'd like to find out what's going on here, what is course/subject/best-reference-mentioned-in-your-notes?
Here's a dumb question: In baby electromagnetism, why does one discuss capacitors in series and parallel when discussing electrostatics (no current moving), only after this then discussing electrokinematics and circuits in series and parallel?
@ACuriousMind : no, footballs don't obey the Lorentz force, but they take a curved path when you put some "side" on the ball. And if you've ever actually played football, you know that the path curves left or right depending on whether you put the side on the ball with your right foot or your left foot. So you're halfway there to understanding the electron and positron motion.
@0celo7 : good boy. Oops, time for my glass of wine before my roast dinner. It's roast chicken today. We had lamb on Wednesday. We'll have pork this Wednesday.
@JohnDuffield since you seem to know about spin can you tell me how spin somehow seems to relate to the fact that a rotation can be expressed as a combination of reflections?
@JohnDuffield what do you mean by saying 'a rotation is a rotation, it isn't a mathematical operation it's a real thing'? Especially as some way to show a rotation can not be decomposed into the composition of reflections... Even a Lorentz transformation is a rotation, which is not intuitive, so I don't get what you're saying, seems like some gut feeling preaching tbh
Can someone tell me the significance of these badges:
Precognitive : Followed the Area 51 proposal for this site before it entered the commitment phase
Beta : Voted 10 times, added 3 posts score > 0, and visited the site on 3 separate days during the private beta
My questions:
What...
I'm going mad about the problem.
I really don't understand why do electron have 1/2 spin number, why they are not actually spinning.
I can accept that the electrons have their own magnetic field, which is certain, but why do they have $\hbar\sqrt3/2$ of angular momentum, and I don't know what t...
