# Spin 1/2

Dear Forum,

I would like to understand what the origin of spin 1/2 is. I read in Feynman's lectures that the origin is related to quantum field theory. I know nothing about quantum field theory. Is there an easy explanation?

Thanks Cabrera

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dextercioby
Homework Helper
The origin of spin is not in quantum field theory, but in ordinary non-relativistis quantum mechanics. The correct treatment of spin 1/2 is found however in quantum field theory. And no, normally there's no easy explanation about this.

Could anybody suggest a link for an introduction in quantum field theory?

regards,
Cabrera

tom.stoer
The shortest explanation I know is related to the structure of the SO(3,1) symmetry group of Minkowski spacetime. On can show that this symmetry group is related to SU(2) * SU(2) which alowes for half-integer representation. That means that Lorentz symmetry allowes for half-integer spins.

The shortest explanation I know is related to the structure of the SO(3,1) symmetry group of Minkowski spacetime. On can show that this symmetry group is related to SU(2) * SU(2) which alowes for half-integer representation. That means that Lorentz symmetry allowes for half-integer spins.
Can any one explain what spin 1, 1/2, -1/2 actually mean?

I'm not asking to know their mathematical origin, but what this spins physically mean?
What physical property a particle has to have to be rewarded with spin 1 or spin 1/2.

photon has spin 1/2
Z boson has spin 1

What physical property Z boson has but photon does not have?
I once read some where, the spin does not mean physical spin of the particle.
Then where does spin angular momentum comes from?

Or is it the other way around? From spin (extra) angular momentum, which is measurable, physicists determine its spin number?

An inquiring mind wants to know.

ZapperZ
Staff Emeritus
Can any one explain what spin 1, 1/2, -1/2 actually mean?

I'm not asking to know their mathematical origin, but what this spins physically mean?
What physical property a particle has to have to be rewarded with spin 1 or spin 1/2.

photon has spin 1/2
Z boson has spin 1

What physical property Z boson has but photon does not have?
I once read some where, the spin does not mean physical spin of the particle.
Then where does spin angular momentum comes from?

Or is it the other way around? From spin (extra) angular momentum, which is measurable, physicists determine its spin number?

An inquiring mind wants to know.
Before you continue with this line of questioning, ask yourself whether you can explain what an apple really means. What is it really?

If you think that you can only explain what an apple is via a list of properties and characteristics on what an apple is, then you have just discovered why what you are requesting makes no sense. To completely rule out the mathematical description of spin is to completely rule out using "fruits" as a category to explain what an apple is.

Zz.

tom.stoer
The problem is that usually we think about orbital angular momentum of a rotating massive body:

$$\vec{L} = \vec{r} \times \vec{p}$$

From this equation we can derive several properties of rbital angular momentum, e.g. that it "generates rotations", that two rotations with different axes of rotation "do not commute", that "orbital angular momentum is consvered" (given that certain symmetries hold) etc. I think in that sense we can explain what spin 1, 1/2, ... actually mean".

Now replace

$$\vec{L} \to \vec{S}$$

$$\ldots = \vec{r} \times \vec{p}$$

while keeping most of the other statements. Now you have to explain again what spin actually means.

I assume you know that the number 1/2, 1 etc just describes the numbering sequence for the quantum states in units of h?
Apart from that, spin is just a quantum property that has some of the characteristics we associate with spinning objects in the big world.

IMO it probably IS spin -it's just that there are so many fine states in a macroscopic object we don't see the quantum effects. Trying to argue it backwards from the macroscopic experience to 'explain' the fundamental behaviour is like trying to stuff smoke back in a cigarette.

for spin 1/2 particles it is necessary to know dirac eqn(weyl eqn for massless spin 1/2) to know what is from which it really comes from.In case,maxwell eqn can also be written in form similar to dirac eqn but it is possible to show that they describe a spin-1 character rather.

I assume you know that the number 1/2, 1 etc just describes the numbering sequence for the quantum states in units of h?
Apart from that, spin is just a quantum property that has some of the characteristics we associate with spinning objects in the big world.

IMO it probably IS spin -it's just that there are so many fine states in a macroscopic object we don't see the quantum effects. Trying to argue it backwards from the macroscopic experience to 'explain' the fundamental behaviour is like trying to stuff smoke back in a cigarette.
In my student years, when dinosaurs roamed the planet, I used to imagine a particle is physically spinning in certain way, back and forth, 180O or 360O, which gives it 1/2, -1/2, 1, etc spin values. That was the only way I could relate this spins to physical world. I think imagination or drawing a mental picture for visualization is a good way to learn about things that we can not see.

Now I see there are many mathematical quantities (or variables) that have no physical counterparts.

tom.stoer
Now I see there are many mathematical quantities (or variables) that have no physical counterparts.
... no [STRIKE]physical[/STRIKE] visualizable counterparts; they are physicakl in the sense that they are measurable![/QUOTE]

photon has spin 1/2
Z boson has spin 1
Photon has spin 1, the same as Z boson. Photon is a boson, so it must have integer spin. Half integer spin is possible only for fermions.

The number 0, 1/2, 1 or 2 tell you how much is the wave function of a particle rotated when you turn it by 360 degrees. Please note this is not about rotating some point like object, byt an actual wave in a field. The wave has a complex phase and this phase is changing if you rotate the wave.

If you rotate the wave by 360 degrees and the wave is rotated only by 50%, this particle has spin 1/2. If the wave is rotated by 100%, the spin is 1. If the wave is rotated by 200% (i.e. the phase changed fully twice during the 360 degree "revolution"), the spin is 2.

So the spin is associated with the structure of the wave and is closely connected to the features of the field. Spin 0 fields are scalar (they have a single value in each point of space), spin 1 fields are vector fields (they have a direction and magnitude in each point of space), spin 2 fields are tensor fields (they are more complicated in each point of space).

Molar
Photon has spin 1, the same as Z boson. Photon is a boson, so it must have integer spin. Half integer spin is possible only for fermions.

The number 0, 1/2, 1 or 2 tell you how much is the wave function of a particle rotated when you turn it by 360 degrees. Please note this is not about rotating some point like object, byt an actual wave in a field. The wave has a complex phase and this phase is changing if you rotate the wave.

If you rotate the wave by 360 degrees and the wave is rotated only by 50%, this particle has spin 1/2. If the wave is rotated by 100%, the spin is 1. If the wave is rotated by 200% (i.e. the phase changed fully twice during the 360 degree "revolution"), the spin is 2.

So the spin is associated with the structure of the wave and is closely connected to the features of the field. Spin 0 fields are scalar (they have a single value in each point of space), spin 1 fields are vector fields (they have a direction and magnitude in each point of space), spin 2 fields are tensor fields (they are more complicated in each point of space).
So "spin" can be visualized as the rotation of the wave function of a particle? That's a good start for me but what "wave function" does something like a proton/neutron have exactly?