Questions tagged [helicity]

In particle physics, helicity is the projection of the angular momentum onto the direction of momentum. For massless spin-1⁄2 particles, helicity is equivalent to the chirality operator multiplied by $\hbar/2$, so may be used for related chirality questions as well.

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72
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8answers
15k 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 $...
30
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4answers
13k 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 ...
21
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2answers
4k views

How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle?

If I've got an instance of a fundamental particle, how can I separate out the measurements of these four quantities? (I think) I understand the theory behind them, and why the particles in the ...
16
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1answer
942 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 ...
13
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1answer
5k views

What is chirality?

I actually wanted to make the title as "What is the difference between chirality and helicity"? But I didn't do that because I don't understand properly what chirality is. I have gone through this ...
13
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1answer
3k views

Why does photon have only two possible eigenvalues of helicity? [duplicate]

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 ...
13
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1answer
1k 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 ...
12
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3answers
4k 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 ...
11
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1answer
2k views

What is polarisation, spin, helicity, chirality and parity?

Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what ...
11
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1answer
833 views

How can we measure chirality in experiments?

Chirality is a concept quite different from helicity. These two concepts only happen to have the same numerical value for massless particles. I understand that we can measure helicity, but how can we ...
10
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2answers
319 views

Why can we approximate massive particles as massless or vice versa?

Our descriptions of massless and massive particles are very different. For example: Massless particles have only two polarizations, which we call helicities. Spin projection on axes different than ...
9
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2answers
3k views

How can helicity be conserved but chirality not?

I read in a book that for $\beta$-decay the electrons have always been found to have an expectation value for their helicity of $h=-v/c$. Then ist is said in the book, that it follows from this ...
9
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1answer
344 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 ...
8
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2answers
4k views

Why photon only have helicity other than spin? [duplicate]

When learning angular momentum in quantum mechanics, a spin 1 particle have 3 states. Then I saw from sakurai's modern quantum mechanics that photon's two polarization are just like spins, but with ...
8
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3answers
1k views

Addition of spin angular momentum for massless particles

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed? If all three polarizations were allowed, this would be an easy ...
8
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0answers
707 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 \...
7
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1answer
920 views

Does the concept of both helicity and chirality make sense for a massive Dirac spinor?

Does the concept of both helicity and chirality make sense for a massive Dirac spinor? A massive electron in the chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What is the ...
7
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0answers
469 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 ...
6
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3answers
4k 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?
6
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2answers
1k 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 ...
6
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2answers
1k 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 ...
6
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0answers
250 views

General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
5
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2answers
866 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 ...
5
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1answer
819 views

Confusion with chirality eigenstates

In the Weyl/chiral basis, the four components of the Dirac spinor represent left-chirality spin up, left-chirality spin down, right-chirality spin up, and right-chirality spin down, respectively. When ...
5
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1answer
265 views

Derivation of conformal generators in spinor helicity formalism

I've been trying for some time to find the expressions for conformal generators of Witten's paper in perturbative Yang-Mills. Given $P_{\alpha \dot{\alpha}} = \lambda_{\alpha} \overline{\lambda}_{\...
5
votes
1answer
838 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 ...
5
votes
3answers
10k views

Helical motion of charged particle in external magnetic field

When an electron moves in uniform external magnetic field, with velocity not perpendicular, I understand that the magnitude of force is only due to the perpendicular component of velocity and is ...
5
votes
1answer
379 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
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1answer
2k 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
2answers
962 views

Helicity of Antiparticles

I'm really confused by the helicity and handeness of antiparticles. Consider the particle case, the plane wave solution is $\psi(x) = u(p)e^{-ip\cdot x}$, where $u^s(p) = \begin{pmatrix} \sqrt{p\...
4
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1answer
1k views

Pion decay: why is the positron electron neutrino decay suppressed?

I'm reading through M. Thomson's Modern Particle Physics to better understand why the positron electron neutrino decay channel is suppressed relative to the muon and muon neutrino decay route. I know ...
4
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2answers
262 views

How are the two independent states of polarization of photon related to the two helicity states?

(1) In the canonical quantization of the free electromagnetic field, the Coulomb gauge condition $$A^0=0,~~ \nabla\cdot\textbf{A}=0\tag{1}$$ implies that the polarization vector $\epsilon^\mu$ ...
4
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1answer
80 views

What is the QED model about half wave plate?

Surely classical electrodynamics (CED) has a good and well-known answer about the change of light polarization in a HWP (or Quarter wave plate). I tried to find how does this look like from point of ...
4
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0answers
120 views

Analogue of helicity in higher dimensions and concrete formula

Consider Poincare group $ISO(1,d-1)$ in some dimension $d>4$. There are two Casimirs. Let's look at massless one-particle states: the little group is $ISO(d-2)$, and if we restrict to finite ...
4
votes
1answer
425 views

Schwartz's book: Spinor-helicity formalism

I'm trying to learn the spinor-helicity formalism from Schwartz's QFT book. His equation 27.44 is describes the annihilation of an electron(1)-positron(2) pair to a muon(3)-antimuon(4) pair. He ...
4
votes
0answers
85 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 ...
3
votes
2answers
585 views

What are the actual transformation properties of Dirac spinors $u_\sigma(p)$?

Let $u_\sigma(p)$ be a Dirac spinor. As far as I know, it transforms under changes of reference frame according to $$ u_\sigma(p)=S(\Lambda)u_\sigma(\Lambda p)\tag{1} $$ where the $\sigma$ label doesn'...
3
votes
1answer
293 views

Helicity quantization of massless particles

In Appendix B of QFT in a nutshell by Zee, a review of group theory is given. In the last paragraph of the appendix on page 533, he briefly discusses the helicity quantization of massless particles. ...
3
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1answer
435 views

An identity for spinor helicity formalism

I have a question about the spinor helicity formalism from arXiv:1308.1697 Denote the massless spin-1/2 fermions as Eqs. (2.10)-(2.11) in that paper $$v_+(p)= \begin{pmatrix} |p]_a \\ 0 \end{...
3
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1answer
195 views

Can photon helicity change in interactions in QED?

I'm wondering if a photon's helicity can change in QED. For example in Compton scattering could the exiting photon have a different helicity than the incoming photon?
3
votes
1answer
560 views

If a neutrino and his antineutrino has different helicity how can it be a possibility that it is a Majorana particle?

All antineutrinos observed thus far possess right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while neutrinos are left-handed. Notwithstanding that it is said ...
3
votes
2answers
591 views

Helicities in electron-positron annihilation

Consider the massless limit of a process in which an electron-positron pair annihilates into a virtual photon - the final state doesn't matter. If the electron is massless (or if the energy is high ...
3
votes
2answers
440 views

What is a linear polarized photon?

According to Dirac a 'linear' polarized photon is a superposition of left and right rotating photons. Here is a puzzling aspect of this superposition. There are dichroic materials which can absorb ...
3
votes
2answers
333 views

Why is the Spin of the photon neglected?

We know photons have spin s=1. However, in Nuclear physics, the conservation of angular momentum in case of Gamma transitions is employed as follows: $$\vec J_i=\vec J_f+\vec L$$ where $J_i$ is the ...
3
votes
1answer
673 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 ...
3
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0answers
370 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 ...
2
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1answer
185 views

$z$ component of angular momentum under Lorentz transformation for massless particle

This question is related to this Helicity states. Suppose we have $k=[\omega,0,0,\omega]$. In Weinberg's book The Quantum Theory of Fields: Volume I he defines the state $|k,\sigma\rangle$ as an ...
2
votes
1answer
208 views

Is there a standard convention for whether the term “handedness” refers to helicity or chirality?

I was under the impression that the "handedness" of a massive spin-1/2 particle refers to its chirality rather than its helicity. This answer, this one and Srednicki's QFT textbook seem to use the ...
2
votes
1answer
236 views

Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
2
votes
1answer
95 views

Helicity amplitudes and muon/electron currents

I have the following helicity spinor: $$ u_R=\sqrt{E} \begin{pmatrix} c \\ se^{i\phi} \\ c \\ se^{i\phi} \end{pmatrix} $$ We take $s=\sin\theta/2$ and $c=\cos\theta/2$. Also, $E$ and $\phi$ are ...