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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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 $... 2answers 4k views How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle? If I've got an instance of a fundamental particle, how can I separate out the measurements of these four quantities? (I think) I understand the theory behind them, and why the particles in the ... 1answer 2k views What is polarisation, spin, helicity, chirality and parity? Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what ... 1answer 3k views Why does photon have only two possible eigenvalues of helicity? [duplicate] Photon is a spin-1 particle. Were it massive, its spin projected along some direction would be either 1, -1, or 0. But photons can only be in an eigenstate of$S_z$with eigenvalue$\pm 1$(z as the ... 4answers 13k views What's the difference between helicity and chirality? When a particle spins in the same direction as its momentum, it has right helicity, and left helicity otherwise. Neutrinos, however, have some kind of inherent helicity called chirality. But they can ... 1answer 823 views Confusion with chirality eigenstates In the Weyl/chiral basis, the four components of the Dirac spinor represent left-chirality spin up, left-chirality spin down, right-chirality spin up, and right-chirality spin down, respectively. When ... 1answer 833 views How can we measure chirality in experiments? Chirality is a concept quite different from helicity. These two concepts only happen to have the same numerical value for massless particles. I understand that we can measure helicity, but how can we ... 3answers 4k views If photons carry 1 spin unit, why does visible light seem to have no angular momentum? Spin 1 silver atoms have a definite spin axis, e.g. up or down along an axis labeled X. This in turn means that they carry angular momentum in an overt, visible fashion. However, spin 1 photons do ... 1answer 2k views Why helicity is proportional to the spin of particle and has two values? How can it be shown without using the little group formalism? Let's have the Wigner's classification for the irreducible represetation of the Poincare group. For the massless case the eigenvalues of ... 3answers 214 views Spin Up with Indefinite Helicity Imagine we are studying the spin quantization along the same axis as the momentum. What if I have a Dirac spinor with a spin up but no definite helicity ($\psi_L,\psi_R\neq0$): $$u(p)= \left(\begin{... 2answers 3k views How can helicity be conserved but chirality not? I read in a book that for \beta-decay the electrons have always been found to have an expectation value for their helicity of h=-v/c. Then ist is said in the book, that it follows from this ... 1answer 1k views What is the difference between the properties of Electron spin and Photon polarization/helicity? What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half? This question stems ... 2answers 591 views What are the actual transformation properties of Dirac spinors u_\sigma(p)? Let u_\sigma(p) be a Dirac spinor. As far as I know, it transforms under changes of reference frame according to$$ u_\sigma(p)=S(\Lambda)u_\sigma(\Lambda p)\tag{1} $$where the \sigma label doesn'... 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 ... 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 ... 1answer 947 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 ... 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 ... 2answers 868 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 ... 1answer 922 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 ... 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 ... 2answers 263 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}$$implies that the polarization vector \epsilon^\mu ... 2answers 1k views Photon spin projection to arbitrary axis For photons (and any massless particle) we consider only a spin projection into the direction of motion (helicity). Why it's meaningless to talk about projection of photon's spin into some arbitrary ... 1answer 838 views Weak interaction and the Chirality of anti-particles Consider a weak current of the form J^{\mu} = \bar{u}_{\nu}\gamma^{\mu}(1-\gamma^5)u_{e} This describes the part of a weak process where a left-handed electron converts into a left-handed ... 2answers 127 views Difference between left- and right-handed, helicity and chirality What is the difference? I know there is the (almost) same question What's the difference between helicity and chirality? but when a particle is given as left-handed. Is it helicity or chirality? 1answer 216 views Why helicity for massless particles is Lorentz invariant? By definition helicity is projection of spin onto the 3 momentum.$$h={\bf J} \cdot {\mathbf{P }} $$where {\mathbf{P }}=(P_1,P_2,P_3) is the momentum operator and {\mathbf{J }}=(J_1,J_2,J_3) ... 1answer 1k views Pion decay: why is the positron electron neutrino decay suppressed? I'm reading through M. Thomson's Modern Particle Physics to better understand why the positron electron neutrino decay channel is suppressed relative to the muon and muon neutrino decay route. I know ... 1answer 208 views Is there a standard convention for whether the term “handedness” refers to helicity or chirality? I was under the impression that the "handedness" of a massive spin-1/2 particle refers to its chirality rather than its helicity. This answer, this one and Srednicki's QFT textbook seem to use the ... 0answers 330 views Spin and polarization, QM vs QFT On page 34 of A. Zee's book QFT in a Nutshell, he states: I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of ... 1answer 95 views Helicity amplitudes and muon/electron currents I have the following helicity spinor:$$ u_R=\sqrt{E} \begin{pmatrix} c \\ se^{i\phi} \\ c \\ se^{i\phi} \end{pmatrix} $$We take s=\sin\theta/2 and c=\cos\theta/2. Also, E and \phi are ... 3answers 318 views Does orbital angular mometum has no meaning for single photons? In the quantization of free electromagnetic field, it is found that the left-circularly polarised photons corrsponds to helicity \vec{S}\cdot\hat p=+\hbar and right-circularly polarised photons ... 1answer 77 views Helicity states On page 71 of Weinberg's book The Quantum Theory of Fields: Volume I, he defines the operators$$A=J_2+K_1$$and$$B=-J_1+K_2$$where${\mathbf{J }}=(J_1,J_2,J_3)$are the rotation generators and${\...
What is the mathematical proof that the helicity of a massive spin-$1/2$ fermion is not Lorentz invariant? Something is Lorentz invariant (e.g., $P_\mu P^\mu$) if it commutes with all the generators ...
Physical polarization vectors are transverse, $p\cdot{\epsilon}=0$, where $p$ is the momentum of a photon and $\epsilon$ is a polarization vector. Physical polarization vectors are unchanged under a ...