Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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.

Filter by
Sorted by
Tagged with
2
votes
2answers
123 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?
2
votes
1answer
184 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 ...
1
vote
1answer
75 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 ${\...
0
votes
1answer
62 views

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 $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
1
vote
1answer
205 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 ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
1
vote
0answers
62 views

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 ...
1
vote
0answers
22 views

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 ...
0
votes
1answer
21 views

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?
1
vote
0answers
25 views

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 ...
0
votes
1answer
141 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,...
2
votes
1answer
34 views

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 ...
1
vote
0answers
23 views

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 ...
2
votes
0answers
84 views

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 ...
1
vote
1answer
58 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 ...
1
vote
1answer
99 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 ...
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 ...
0
votes
0answers
254 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 ...
2
votes
1answer
121 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 ...
0
votes
1answer
81 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_{...
1
vote
1answer
99 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 $s$, ...
0
votes
0answers
59 views

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{...
1
vote
1answer
121 views

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 ...
1
vote
3answers
456 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 ...
0
votes
1answer
180 views

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?
1
vote
2answers
102 views

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 ...
2
votes
0answers
128 views

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 $u^\pm$ ...
1
vote
0answers
155 views

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 ...
0
votes
0answers
154 views

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 ...
0
votes
1answer
735 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 ...
0
votes
2answers
144 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{\...
4
votes
2answers
257 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 $\epsilon^\mu$ ...
0
votes
1answer
79 views

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 ...
0
votes
1answer
79 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. ...
0
votes
3answers
211 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{...
0
votes
0answers
73 views

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 ...
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. ...
1
vote
2answers
154 views

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 ...
0
votes
1answer
395 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 ...
1
vote
1answer
336 views

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). ...
0
votes
0answers
300 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. ...
0
votes
1answer
279 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 $\not p=p^\mu \eta_{\mu\nu}\gamma^\nu$ ...
1
vote
0answers
89 views

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 ...
1
vote
0answers
278 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_\...
4
votes
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 ...
2
votes
0answers
346 views

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 ...
0
votes
1answer
74 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 ...
4
votes
2answers
937 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\...
3
votes
1answer
194 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?
1
vote
1answer
135 views

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 ...
1
vote
2answers
634 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 ...