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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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Tensor decomposition v.s helicity amplitude

It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g via explicit tensor decomposition $$\Pi^{\mu \...
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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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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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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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68 views

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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119 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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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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93 views

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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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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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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Helicity conservation and proof $\phi_L^*\phi_R-\phi^*_R\phi_L=0$

Helicity was defined as below: $E\xi=\pm\sigma\cdot p \xi$ where $p$ was the momentum operator and $E$ was the energy operator, $\sigma$ was the Pauli matrix. $\displaystyle H=\frac{\sigma\cdot p}{|p|...
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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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316 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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593 views

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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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 $\epsilon^\mu$ ...
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Is a (Dirac) Particle Where $\vec{p} = (p^1,0,0)$ in an Eigenstate of Helicity? [closed]

Is a particle where $\vec{p} = (p^1,0,0)$ an eigenstate of the helicity operator? First, can I determine this without doing the math? Second, I also wanna prove it mathematically but doing the math ...
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68 views

Labelling of states using $R$-symmetry for ${\cal N=4}$ SUSY

In Modern Supersymmetry by John Terning, page 13, the states of the massless supermultiplets of $N=4$ SUSY are labelled by the helicity and representation of R-symmetry under which they transform. ...
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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{...
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Do gluons have only two possible eigenvalues of helicity?

In the Standard Model, gluons are massless spin-1 bosons just as photons are, so it stands to reason that they only have two possible eigenvalues of helicity for the same reason that photons, which ...
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268 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. ...
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Polarization state of a photon

From the book "Quantum Field theory and the Standard Model": "It is known that light has two states of polarization". What does this statement mean? What are the two states of polarization and how ...
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293 views

What are the differences between chiral states and helical states in condensed matter physics?

As we know in particle physics, chirality corresponds to eigenvalues of the fifth gamma matrix, and helicity corresponds to the value of the projection of spin onto momentum. So in condensed matter ...
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Why is helicity important in quantum field theory?

What makes helicity an important quantity in quantum field theory? I know that one can classify particles by mass and spin. For particles without mass one uses helicity (correct me if this is wrong). ...
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254 views

Helicity of Massless Particles

A well-known result of Wigner's classification of relativistic particles is that massless particles transform with helicity $h \oplus -h$ under $ISO(2)$. Thus, such particles have two helicity states. ...
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259 views

Trace technology with polarisation vectors

Consider $d$-dimensional gamma matrix structures. I have an expression like $$ \sum_{h_2=\pm}\text{Tr}(\not{\xi}_2\not{p}_3\bar{\not{\xi}}_2\not{p}_1), $$ where $\not p=p^\mu \eta_{\mu\nu}\gamma^\nu$ ...
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Weinberg soft factor in spinor helicity

The leading order Weinberg soft factor is found to be $$\displaystyle\sum_{a=1}^{n}\frac{\epsilon^{\mu\nu}p_{\mu}p_{\nu}}{q.k_a},$$ where $a$ labels the external particles and $p$ denotes the ...
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258 views

Showing Parity violation in muon decay

An exam question reads; By considering the helicity of the decay products, and the conservation of angular momentum, show that the high energy positrons in the reaction $\mu^+ \to e^++\nu _e +\nu_\...
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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 ...
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Parity of photon helicity state

This question is fundamental enough and I probably should know the answer at this point, but for some reason I am confused. I know that helicity states should go into each other under parity transform ...
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1answer
65 views

Nature of Chirality: Additive or multiplicative?

What kind of quantum number is Chirality? Helicity, being the projection of spin in the direction of the momentum, is like a component of spin, and therefore, additive in nature. For a process, $A\to ...
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785 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\...
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176 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?
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Density Matrix for the Relativistic Spin Tensor

In quantum we have a density matrix for the spin states. The density matrix allows us to specify both polarized states, but also various levels of polarization. The relativistic version of the ...
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477 views

Transverse polarizations of a massless spin 1 particle

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 ...
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229 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}_{\...
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General Relativity and spin/helicity two massless particle

I usually read that GR can be thought of as the unique theory of a massless spin-2 particle (I think that this is the graviton). I know that GR is the unique theory that has: diffeomorphism ...
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Helicicity operator of a particle

How can one project the spin of a particle along the direction of momentum as they belong to different bases? Or is it allowed because there are infinitely many bases connected through similarity ...
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93 views

How strong are the experimental constraints on the neutrino helicity really?

It is commonly accepted that all neutrinos have left-handed helicity and all anti-neutrinos are right-handed helicity.$^1$ The experimental base comes from Goldhaber's famous experiment performed in ...