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10
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1answer
88 views

Chirality, helicity and the weak interaction

From what I'm understanding about Dirac spinors, using the Weyl basis for the $\gamma$ matrices the first two components behave as a left handed Weyl spinor, while the third and the fourth form a ...
1
vote
0answers
46 views

If a photon is a boson and has spin 1, shouldn't it have 3 spin orientations since spin 1 is a triplet? [duplicate]

I've gotten used to the fact that a spin can be described by its total spin and its $z$-component. And I've learned that a particle (really, anything) with spin 1 forms a triplet with three possible ...
1
vote
0answers
29 views

Chirality and helicity

I have massless Dirac equation and chirality and helicity operators which are given as $$ \hat {P}_{ch}\Psi = \gamma_{5}\Psi, \quad \hat {P}_{h}\Psi = \frac{(\hat {\mathbf S} \cdot \mathbf ...
2
votes
0answers
48 views

The question about Lorentz invariance of the helicity quantum number for the massless particles

I need to show that helicity is Lorentz invariant (under the proper Lorentz transformation) for the massless particles. I heard about most frequently used argument which contains an idea of ...
5
votes
1answer
132 views

Orbital angular momentum of photon

People talk about orbital angular momentum (OAM) of photons. Is there some physical example that cannot be explained without assuming that photons have non-zero OAM? Does different photons have ...
3
votes
1answer
85 views

Helicity and Chirality

Does the concept of both helicity and and chirality make sense for a massive Dirac spinor? A massive electron in chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What are the ...
3
votes
0answers
105 views

Reducing massive representation of the Poincare group to the massless one

I want to ask about the connection for massive and massless representation of the Poincare group. Sorry for the awkwardness. First I must to represent the formalism for both of cases. Massive ...
1
vote
2answers
203 views

Why does the Standard Model predict Neutrinos are massless?

Why are neutrinos massless in the Standard Model? Is it connected with experimental fact that neutrinos always have only one direction of projection of spin on motion direction?
7
votes
1answer
147 views

Is the third spin vector of a photon always suppressed?

I like to tell people interested in light polarization that the photon is a vector boson for which the third spin axis, the one in the direction of travel, is suppressed due to photons being massless ...
0
votes
0answers
72 views

Photons angular momentum / spin

I have a textbook that says that photons have a spin of absolute value $\hbar$ and at some other point, they say that it has angular momentum of absolute value $\hbar$. Now, since they are different ...
1
vote
1answer
158 views

Maxwell's equations as the particular case of massive vector field equation

There was a discussion (please look to the comments on my answer) about getting Maxwell's equations for free spin-1 field by using massive spin-1 representation's equations. I'll start from the ...
1
vote
1answer
136 views

Coulomb gauge and two degrees of freedom of EM field

The EM field has two possible polarizations, which is caused by spin-one nature of field (leads to the Lorenz gauge) and massless of the field. Really, the Klein-Gordon equations for the EM field $$ ...
3
votes
1answer
154 views

Weak interaction and the Chirality of anti-particles

Consider a weak current of the form $ J^{\mu} = \bar{u}_{\nu}\gamma^{\mu}(1-\gamma^5)u_{e} $ This describes the part of a weak process where a left-handed electron converts into a left-handed ...
4
votes
0answers
149 views

Chirality and helicity operators for the massless bispinor rep and their generalisation on arbitrary (tensor, 4-vector etc) cases

Let's have chirality projection operator $$ \hat {C}_{\pm} = \frac{1 \pm \gamma^{5}}{2}. $$ We introduce it and called it chirality, because $$ \hat {C}_{+}\psi = \begin{pmatrix} \psi_{\alpha} \\ 0 ...
6
votes
3answers
708 views

If photons carry 1 spin unit, why does visible light seem to have no angular momentum?

Spin 1 silver atoms have a definite spin axis, e.g. up or down along an axis labeled X. This in turn means that they carry angular momentum in an overt, visible fashion. However, spin 1 photons do ...
3
votes
0answers
142 views

Chirality, helicity and their relationship for the massless case

Chirality can be interpreted as a property of Lorentz group - Lorentz transformation of field through representation $(s, 0)$ or representation $(0, s)$. For the massless particles one says, that ...
3
votes
1answer
353 views

Why helicity is proportional to the spin of particle and has two values?

How can it be shown without using the little group formalism? Let's have the Wigner's classification for the irreducible represetation of the Poincare group. For the massless case the eigenvalues of ...
4
votes
1answer
112 views

Helicity Representation of Massive Spinor

For massless spinors case we can decompose momentum into Weyl sub-parts as $$p = \lambda_{a}\tilde \lambda_{\dot a}.$$ But for the case of massive fermions can I do something like this? Decompose ...
4
votes
0answers
56 views

Helicity dependence in loop diagrams

I am trying to evaluate a diagram that looks like The middle of the diagram is a fermion loop. I know that the coupling between the $Z^0$ and fermions depends on the fermions' helicities, so it ...
1
vote
2answers
226 views

Doubts concerning Wigner's classification

Wigner classified particles in function of the eigenvalues of $P_\mu P^\mu$ and $W_\mu W^\mu$. Then, it can be proved that for massless particles spin values can be only $\pm s_{max}$. But for a ...
2
votes
0answers
74 views

Helicity for Zero Rest Mass Field Equations

I'm trying to reconcile the usual definition of the helicity operator, namely $$ h = \hat{p}.S$$ with the definition of a massless helicity $n$ field as a symmetric spinor field $\phi^{A\dots B}$ ...
1
vote
0answers
177 views

Helicity operator in Non relativistic limit

Helicity operator in Dirac equation is given by $$H=\frac{\vec{S}\times \vec{P}}{P^{2}}$$ This operator commutes with dirac hamiltonian.We can also define a helicity(with same form) operator in case ...
8
votes
0answers
452 views

What is the difference between the properties of Electron spin and Photon polarization/helicity?

What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half? This question stems ...
17
votes
4answers
1k views

Why is the $S_{z} =0$ state forbidden for photons?

If photons are spin-1 bosons, then doesn't quantum mechanics imply that the allowed values for the z-component of spin (in units of $\hbar$) are -1, 0, and 1? Why then in practice do we only use the ...
6
votes
1answer
835 views

Why does photon have only two possible eigenvalues of helicity?

Photon is a spin-1 particle. Were it massive, its spin projected along some direction would be either 1, -1, or 0. But photons can only be in an eigenstate of $S_z$ with eigenvalue $\pm 1$ (z as the ...
5
votes
2answers
507 views

Feynman rules with helicity states.

Whenever Feynman rules are stated they are always without any mention of the helicities - this I find to be very confusing. How does one introduce and account for that? Is there an intuitive/simple ...
2
votes
1answer
516 views

Photon spin projection to arbitrary axis

For photons (and any massless particle) we consider only a spin projection into the direction of motion (helicity). Why it's meaningless to talk about projection of photon's spin into some arbitrary ...
10
votes
1answer
837 views

How does one experimentally determine chirality, helicity, spin and angular momentum?

If I've got an instance of a fundamental particle, how can I separate out the measurements of these three concepts? (I think) I understand the theory behind them, and why the particles in the ...
10
votes
2answers
2k views

What's the difference between helicity and chirality?

When a particle spins in the same direction as its momentum, it has right helicity, and left helicity otherwise. Neutrinos, however, have some kind of inherent helicity called chirality. But they can ...