# Particle spin

1. Dec 30, 2004

### tozhan

is fermonic spin the same as polarisation of a particle?

example of what i mean. When light is reflected it comes partly polarised right? this means only some photons are reflected along a certain plane.

does this difference in polarisation affect the way the particles interact with other particles and the higgs field? ie, photons dont interact with the higgs field however electrons do so they therefore have difference spin or polarisation. is this right?

Tom

2. Dec 30, 2004

### marlon

Polarization has different definitions. It can be the plane in which the electric field "vibrates" as a part of the electromagnetic wave...When you are talking about circular polarization for example you are referring to this definition. Polarization however is also the total electrical dipole moment per unit of volume in electrostativs. For example when you apply an electrical field onto some object it can become polarized. This means that the charges in this object will direct themselves in a certain direction because of the external applied field.

Photons do not interct with the Higgs field because they exhibit the socalled U(1)-symmetry of the electromagnetic interaction. Basically this means that the equations decsribing these interactions have a certain local symmetry which is called U(1). this has NOTHING to do with polarization however...

In the case of fermions it is true that only left handed fermions will feel the weak interactions like beta-decay. But this applies to chirality and not polarization...Chirality basically is the connection between the direction of propagation of the fermion with its spin.

regards
marlon

3. Jan 5, 2005

### tozhan

ok thanks, can you give an explanation of why in any quantum energy level there are two 'types' of electron, $$s_z=+\frac{1}{2}$$ and $$s_z=-\frac{1}{2}$$ and yet i was told all 'naturally' occuring electrons spin to the left!? was i being lied to or am i missing something? :uhh:

is it only when electrons are free of a nucleus that they are always spin +1/2?

4. Jan 7, 2005

### marlon

Well you are referring to what is called the spin quatntum number s. Basically what it indicates is the direction of rotation of some particle along its axis. So spin up (denoted by $$s_z = 1/2$$) means that the particle rotates counterclockwise...But there is one important aspect here : i talked about SPIN UP. Now you can ask what is the UP-direction ? What is your frame of reference here. Well, it is the direction of some extern applied magnetic field. So spin up means that your rotationaxis is positioned along the direction of the magnetic field. Without the presence of this magnetic field, the spin quantum number doesn't indicate anything because you don't have no frame of reference.

This external field can come from the "nearby" nucleus in some atom. So when an elecrton is certain values for it's spin quantum number, this is a result from the fact that there is some interaction of the electron with the atomic nucleus. This interaction is described in terms of the spin (=electron)and the magnetic field (atomic nucleus). Thus, you now have a system that enables you to describe such nuclear interactions and that is what QM does. Keep in mind that not only electrons have spin, but every elementary particle has spin. Particles with integer spin are called bosons (like the foton) and particles with spin like the electron (1/2, ...) are called fermions. Conclusion : electrons cannot be described in terms of their spin because this spin needs to be expressed in terms of the direction of some external magnetic field (coming from the nearby atomic nucleus, for example)

regards
marlon

Last edited: Jan 7, 2005
5. Jan 7, 2005

### dextercioby

Beautiful exposure,wrong conclusion.Electrons (and generally massive leptons) are irreductible massive representations of spin 1/2 of the Poincaré group.A quantum state (a state in the separable Hilbert space of the representation) is completely specified by three numbers representing the three compnents of the particle's (electron's) linear momentum and a number which is the eigenvalue of the $\hat{S}_{z}$,which,in this case,can be only either 1/2,or -1/2.
To give the eq.
$$\hat{\vec{P}}^{2}|\vec{p},\pm\frac{1}{2}\rangle=m^{2}|\vec{p},\pm\frac{1}{2}\rangle$$ (1)

$$\hat{\vec{W}}^{2}|\vec{p},\pm\frac{1}{2}\rangle=-m^{2}\frac{1}{2}(\frac{1}{2}+1)|\vec{p},\pm\frac{1}{2}\rangle$$(2)

$$\hat{\vec{P}}|\vec{p},\pm\frac{1}{2}\rangle=\vec{p}|\vec{p},\pm\frac{1}{2}\rangle$$ (3)

$$\hat{P}^{0}|\vec{p},\pm\frac{1}{2}\rangle=\bar{p}^{0}|\vec{p},\pm\frac{1}{2}\rangle$$ (4)

$$\hat{\vec{W}}\cdot\hat{\vec{N}} |\vec{p},\pm\frac{1}{2}\rangle=-m(\pm\frac{1}{2}) |\vec{p},\pm\frac{1}{2}\rangle$$ (5)

,where
$$\bar{p}^{0}=:\pm p^{0}=\pm \sqrt{\vec{p}^{2}+m^{2}}$$ (6).

I've always thought these things were piece of cake compared to string theory and gravitons.

Daniel.

PS.The $\pm$ from (6) is unrelated to the one in the state vectors (which would correspond to the 2 possible values of $m_{s}$).

Last edited: Jan 7, 2005
6. Jan 7, 2005

### marlon

How am I wrong? You are getting off track here... I wasn't talking about how to describe some quantumstate and what the necessary prerequisites therfore were. I am merely stating that for spin to "manifest" itself, you need an external magnetic field...Spin just like the spin orbit coupling or whatever coupling you consider ONLY exists as a result of interaction of some particle with other surrounding particles.

how do you mean ???

regards
marlon

7. Jan 7, 2005

### marlon

then you are wrong because they are "in fondo" exactly the same...

marlon

8. Jan 7, 2005

### marlon

Nice copy out of your QM-textbook but not very refreshing i am afraid ...But this is not the point here...you are already working with spin quantumnumbers because you know they exist and you know what influence they have on the energy-levels. I ask you this question : how can you show this correct theory experimentally. The answer to this question is also the justification for my post on what SPIN UP means. This is the point i was trying to make, but you clearly missed it. WHAT IS UP ???

regards
marlon

9. Jan 7, 2005

### dextercioby

I think i just proved to you;take the quote:
I believe i just proved you wrong...Wrong not only the first sentance,but the second as well.Spin doesn't 'need' to be expressed in term of the direction of an generally inexistent field.U just need an inertial reference frame and 3 orthonormal coordinates and u can build spin theory without any problem.

What does external B have to do with the theoy of Wigner and free electrons??BTW,even if those electrons weren't free and were interacting,their quantum state would still be described by momentum,sign of p_{0} and spin.

I guess i don't need an extra pair of glasses to see what u were talking about. :tongue2:

Your notion of "manifest" is far too different from mine and that's why i'll simply state:you're right... :tongue2:

Marlon,i didn't consider any coupling...Spin exists without the particle's interaction.Jesus,has someone else hacked into your PF account ?? :tongue2:
I bet it does...

Daniel.

10. Jan 7, 2005

### marlon

Again a flaw in your communication. No the quote is no proof...you claimed it was wrong but why...is your word the truth Mr God ???

Generally inexistent??? You don't seem to get the point...Again i ask you the question : WHAT IS "UP" ??? What do you think the x y and z-axis represent ??? What is the physical interpretation of this, you think ???

Ever heard of the Zeemann-effect ??? There is your answer...

:surprised :surprised
haha this is just wrong man ...
even my ignorant hacker thinks that...Really, spin can be reprented via group theory, which on itself is based upon symmetry...It is because of the change in symmetry occuring when an external magnetic field is applied that spin quantumnumbers are calculated...

Please, review your group theory because you seem to have forgotten it...

ps : this was some advice from my hacker mr Wigner....

marlon

Thanks for prooving my point...

11. Jan 7, 2005

### dextercioby

1.I feel ashamed. I guess all this time i've mistakenly taken u as a theorist... :tongue2:
2.It's from a chapter of Bailin & Love's:"Weak interactions",chapter which i translated and addapted into an article for personal use only. :tongue2:
3.Let's not drift with discussion in the experimental part.I don't feel too comfortable speaking about particle phyiscs experiments...As u might have noticed,i agreed to your exposure,found it correct and interesting,but disagreed with your TOTALLY ERRONEOUS CONCLUSION.Actually,yer conclusion had little to do with the contents.You were never speaking about free electrons.So,judging only interacting electrons,how (logically) could u come up with a conclusion concerning free electrons??? It's elementary logics,Marlon...

Daniel.

PS.
:surprised Surely someone else has posted this nonsense.It's not Marlon that i know...Did u ever compute the velocity of rotation?U know,like the Earth's 465ms^{-1} at the equator??

12. Jan 7, 2005

### marlon

That is what we call an easy way out. Sorry about your emotional condition when speaking about such topics but they however cannot be disregarded and they prove my point...It is not all theory my dear boy and certainly not all WRONG theory or WRONG theory-interpretations...

?????????What And this would be your 5th flaw in this thread my dear friend. You didn't get the point at all. That is no good position for debating. Please reread my post man...i am not gonna repeat myself 500 times, that is not eerrr interesting

Wrong again, it is about reading correctly...Daniel

marlon

13. Jan 7, 2005

### marlon

Point is that spin is always an inherent physical property of particles but when you wanna see the influence of this spin (and thus its manifestation on the real time behaviour of particles like energylevels for example) you will need and external field. Otherwise these spin-energylevels are degenerate and no splitting of energylevels shall occur. That does not mean the spin ain't there no more...

learn from this Daniel

Besides the example of rotation-direction was just an analogy...but i guess you didn't see that...in the future i will mention that more clearly for you... no problem...

marlon

14. Jan 7, 2005

### dextercioby

No,is yours???

Oh,but i do...Have u ever heard of "quantum free field theory??"Does Dirac's free field theory (which account for massive charged leptons) involve a B and i didn't see it???

Who said anything about "UP"??It's spin +1/2 or spin -1/2?It's never UP/DOWN.

I'm not sure,here... I'll take a guess...Axis of an orthonormal system of coordinates attached to an inertial reference system??

I did.Two years ago...But it's irrelevant.You wish u discuss interating electrons,i want to discuss free electrons,because that's what it got everything started...

Please,let's not go into that old discussion symmetry-group theory-angular momentum Lie algebra irreductible representations.We didn't agree last time...

I would still have done it,since i have to take (and hopefully pass) an exam in group theory and symmetries...

I know i make bad jokes,but you messin'em up even more makes me feel real sad...

Daniel.

Last edited: Jan 7, 2005
15. Jan 8, 2005

### marlon

:surprised
What's that got to do with anything ???
Besides, i think it would be more appropriate if i'd ask this question to you. Do you even know what QFT is ??? This discussion has only to do with quantummechanics. Please, stop making statements you know nothing about...it makes you sound...well...

So SPIN UP does not mean anything ??? What, do you think, is the mechanism that decides the specific values of the magnetic and spin quantumnumber ???

What is the physical interpretation of calculating Clebsch-Gordan coëfficients ???

Are you ever ???

i refer to your post in the does the earth rotate thread.

Really??? hmmmm;;let's not get into that

ohh come on...you know very well what i am referring to...Please stop arguing just for the sake of arguing.

??? What is there to agree about. This is a mathematical model and your opinion on it is irrelevant. In the previous discussion YOU again mage some false assumptions and statements on how group theory works...That is why Humanino and I responded...Again this is just arguing for the sake of arguing...

Good luck, you are gonna need it... i hope they don't ask spin-related questions...

marlon