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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What is the action of the field $\Psi_L$ on vacuum?

Please help me to understand the following situation. A fermion field $\Psi(x)$ acting on the vacuum can destroy a particle and create an antiparticle. If however, a chiral field $\Psi_L$ defined as $\...
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How to prove that helicity is conserved for massive Dirac particles

The helicity is defined as: $$h=\frac{\vec{S}.\vec{p}}{||\vec{p}||}$$ where $$S= \frac{\hbar}{2} \zeta$$ and $\zeta$ equals \begin{pmatrix} \vec{\sigma} & 0\\ 0 & \vec{\sigma} \end{pmatrix} ...
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Elvang and Huang sign error? Polarization Vectors in the Spinor Helicity Formalism

I am reading through Elvang and Huang's treatment of polarization vectors for all outgoing spin-1 massless particles (metric signature $(-,+,+,+)$). It is given in Eq. (2.50) in the PDF (but Eq. (2.51)...
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Spinor Helicity Formalism: Reference Spinors $q$ in Compton Scattering

My question is rather straight forward, but the setup in order to pose the question is a little lengthy; please bear with me! I am trying to calculate the average over initial states and sum over ...
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Why, if photons have their spin in the same direction of the electrons, the formers will less likely be able to flip the spins of the latters

It's about the Goldhaber experiment, where the exercise I'm trying to solve is: Photons are filtered according to their helicity thanks to the magnetic field. For a given magnetic field, the electrons ...
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What would Maxwell's equations look like if photons had only a single helicity?

There are two types of photons, positive and negative helicity photons. What would Maxwell's equations look like say if there were only negative helicity photons? It would be interesting to see this ...
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How can higher-energy beta decays have 'higher polarization'?

The higher the energy of the particles, the higher their polarization. I just cut-and-pasted the above statement from the chirality-and-helicity section of the Wiki article on 'Beta decay'. What does ...
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Goldhaber experiment - Why are there only left-handed neutrinos?

"From the Goldhaber experiment we can deduce that there are only left handed neutrinos." I don't understand this. Can't we find an experiment that only produces overwhelmingly right handed ...
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Eigenspinor of helicity of electrons

I am reading the chapter in Griffth's introduction to elementary particle. By solving the momentum space Dirac equation and requiring the solution of the spinor to be the eigenspinor of the helicity ...
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Helicity Problem

I have the following task and I have no idea how to start. To do: The angular momentum of the radiation field is given by $$ J = \int x \wedge (E \wedge B) d^3x $$ Define the corresponding operator. ...
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Neutrino Helicity and Uncertainty

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase Neutrino are left-handed. The spin is in the opposite direction of motion. ...
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Helicity and chirality of particles in the pion decay

Let us consider the $\pi^+$ decay: $$\pi^+(q) \rightarrow \nu_\mu(p_1) + \mu^+(p_2)$$ In the Standard Model, the neutrinos are left-handed. Since they are massless, chirality corresponds to helicity. ...
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Dirac sea interpretation VS the Feynman-Stueckelberg interpretation for antiparticles

I am trying to understand the difference between the Dirac sea interpretation and the Feynman–Stueckelberg interpretation of the negative energy solutions of the Dirac equation. To do so, I would like ...
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What are differences among chiral, helical and spiral in quantum spin context?

For chiral, as far as I know, there are vector chirality $\kappa_{ij}=\mathbf{S}_{i}\times \mathbf{S}_{j}$ which characterizes non-collinear spin arrangement and scalar chirality $\chi_{ijk}=\mathbf{S}...
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Colour-ordering formula of QCD amplitudes (tree-level)

I have been studying colour-ordered amplitudes and spinor helicity formalism for a while. It is now apparent to me that I do not fully understand the 'master' formula which allows us to relate the ...
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Angular distribution of neutrinos in $e^-u\rightarrow\nu_ed$ scattering

What does the angular distribution of the neutrinos look like in the scattering $e^-u\rightarrow\nu_ed$? The tree-level Feynman diagram looks like this and since all of the fermions couple to a $W$ ...
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Helicity combinations in $gg\rightarrow t\bar{t}$

So, I am trying to understand what helicity combinations can occur in the outgoing top-antitop pair in the tree-level scattering $gg\rightarrow t\bar{t}$. There are 3 diagrams to consider (see below), ...
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Confusion about $1/|\vec{p}|$ in helicity operator

The helicity operator is defined as $$ h = \frac{1}{|\vec{p}|} \vec{\sigma} \cdot \hat{\vec{p}} $$ One of the first exercises into QED is to check whether this commutes with the Dirac Hamiltonian. ...
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What is the value of $W_\mu W^\mu$ for massless particles?

What is the value of the quantity $W_\mu W^\mu$ for massless particles where $W^\mu$ is called Pauli-Lubanski vector defined as $W^\mu=\frac{1}{2}\epsilon^{\mu\nu\alpha\beta}P_\nu J_{\alpha\beta}$. ...
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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?
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$z$ 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 ...
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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 ${\...
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Helicity under rotation

Suppose that the state $|p,\sigma\rangle$ (for a massless particle) has 3 momentum ${\bf p}=p_3$ (that is the momentum is in the $z$ direction) and that $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
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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 ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
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Viscous losses in loop helical flow

Imagine flow of the following kind. The flow line for each flow particle is a helix with its axis bent so that the beginning attaches to the end. How can I determine the viscous losses in this flow ...
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Why does the renormalizable theory have only those particles with helicity less than or equal to 1?

Let the helicity operator be $\frac{P \cdot J}{P^0}$ with an eigenvalue $\lambda$. Then why do renormalizable theories have $|\lambda| \le 1?$ (in general dimensions or in 4ds?) Also, what is the ...
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How do the vector and scalar potentials transform under electromagnetic duality trnasfotmation?

Maxwell equations are invariant under the duality transformation. The electric and magnetic fields are defined in terms of these potentials. How do these potentials transform under duality?
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Four-brackets (Hodges, Momentum Twistors)

I use the reference from Andrew Hodges, available at https://arxiv.org/abs/0905.1473. I am having trouble understanding his use of the four-bracket. I refer to equation 6 and equation 9, where he ...
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220 views

Spin (helicity) and polarizations of photons: are they secretly related?

Edit Circularly polarized photons have $$\textbf{S}\cdot\hat{\textbf{p}}=\pm \hbar\tag{1}$$ and it also satisfies $$\boldsymbol{\epsilon}\cdot\hat{\textbf{p}}=0\tag{2}$$ where $\textbf{S}$ is the spin,...
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Adding helicities

The background: I am looking at Compton scattering in its most general form with $p+\gamma^*\rightarrow p'+\gamma'^*$ in the Breit-frame (which implies that in my case $\vec{p} = -\vec{p}'$). The ...
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How to determine the squared average amplitude for $\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$?

I have the following charged current interaction, at quark level, by the process: $$\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$$ By assuming that the energy is such that I can neglect the lepton and ...
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Can spherical harmonics be used in relativity equations?

I have a neutral pion of mass $m_{\pi}$, and it decays into two photons. In it's reference frame the decay is isotropic. One of the photons has a helicity of $+\hbar$ and the other $-\hbar$. In ...
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78 views

Helicity is invariant under boosts along $\hat{p}$?

In this source (In Introduction, p. 1) we find the claim that the helicity operator $h=\vec{S}\cdot\hat{p}$ is invariant under rotations and boosts. I agree that is is clearly invariant under ...
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Spin-helicity formalism for gluon-gluon amplitudes

In Schwarz's QFT he introduces in chapter 27 the Spin-Helicity formalism as a way of calculating gluon-gluon interactions much easier than going through all the Feynman calculus from the beginning to ...
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248 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 ...
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345 views

Helicity: massive vs massless particles

Usually massive particles can be described as eigenstates $|p,\lambda\rangle$ of the angular $J^3$ operator, while massless particles are eigenstates $|p (m=0),\lambda\rangle$ of the helicity operator ...
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Photons have Spin 1 - Franz Gross' Relativistic Quantum mechanics and Field Theory

I've got a question regarding the derivation of spin 1 for photons in Franz Gross' Relativistic Quantum Mechanics and Field Theory. From pages 50 to 56 he attempts to derive "how this [spin 1] comes ...
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118 views

Vector Spherical Harmonics and total angular momentum

In their book Akhiezer et al. give a definition of vector spherical harmonics (p.18 of Russian Edition) as $$\pmb{Y}_{j\ell m}(\pmb \Omega) = \sum_{m' \lambda} \langle \ell m' 1\lambda| jm \rangle Y_{...
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108 views

Prove Spin of a massless particle $S_z=\pm1$

Quote from Introduction to High Energy Physics Edition 4 by Donald H. Perkins chapter 3.3.1 "It can be proved as a consequence of relativistic invariance that for any massless particle of spin $s$, ...
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Conserved quantity in Graphene

The computation of the band structure of Graphene basically leads to the diagonalization of the following Hamiltonian: $$ H = -t \left( \begin{array}{cc} 0 & \epsilon(\vec{k}) \\ \epsilon^*(\vec{...
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Helicity in Graphene

In Graphene, there are two independent points, the Dirac points, where the conduction and the valence band touch. Let's call these points $K_+$ and $K_-$. In a low-energy description, the Hamiltonians ...
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600 views

Mathematical proof on helicity of a massive fermion is not Lorentz invariant

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 ...
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Neutrino helicity

Neutrinos are produced in beta decays with a given helicity. My question is wether this helicity is a constant of this movement or is it variable?
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Spinor helicity relation with photon emission

Consider an electron emitting a single photon. There is exactly one gamma matrix (corresponding to the photon vertex) between the outgoing spinor $\bar{u}$ and incoming spinor $u$. This implies that ...
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Why are antiparticles associated with spin-flipped spinors?

In section 2.2 of Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity (http://arXiv.org/abs/1308.1697), beneath equation (2.9), it is mentioned that $u^{\pm}=v^{\mp}$, where $u^\pm$ ...
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Spin vs Helicity conservation

I am a bit confused about spin conservation at relativistic energies. I am reading a QFT book by Peskin and at a point he specifies that "In the nonrelativistic limit the total spin of the system is ...
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Why if 2 operators commute they have a common set of eigenvectors and what's the relation to 2 fold degeneracy?

I have the following sentence in my lecture notes "Dirac hamiltonian and helicity have a common set of eigenvectors, this is also the reason for the two fold degeneracy found for every energy ...
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What is the helicity of a particle at rest?

Given the definition of helicity as $\lambda = \vec{p} \cdot \vec{J}$ up to normalization, does it even make sense to define helicity for a particle at rest (i.e. $\vec{p} = 0$)? If it doesn't make ...
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174 views

What does the non-Lorentz indices $\lambda$ of the polarization vector $\boldsymbol{\epsilon}_\lambda$ count?

The Fourier mode expansion of the free electromagnetic field in radiation gauge is given by $$\textbf{A}(x)=\int\frac{d^3p}{(2\pi)^3\sqrt{2\omega_\textbf{p}}}\sum\limits_{\lambda=1,2}[\boldsymbol{\...
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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 $\epsilon^\mu$ ...