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
0
votes
0answers
27 views

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}...
1
vote
0answers
25 views

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 ...
5
votes
1answer
187 views

NMHV 5 Gluon Scattering (Elvang and Huang, Ex 3.11)

In Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity, Exercise (3.10) (Exercise (3.11) in the printed version) asks the reader to construct the NMHV scattering amplitude of five ...
32
votes
5answers
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 ...
0
votes
1answer
47 views

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), ...
0
votes
0answers
24 views

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 $W$ ...
1
vote
1answer
70 views

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. ...
4
votes
1answer
458 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 ...
0
votes
1answer
173 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,...
1
vote
1answer
87 views

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 $W^\mu=\frac{1}{2}\epsilon^{\mu\nu\alpha\beta}P_\nu J_{\alpha\beta}$. ...
3
votes
1answer
696 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 ...
2
votes
2answers
191 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
199 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
80 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
72 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 $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
0
votes
1answer
251 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 ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
0
votes
2answers
179 views

Photon carries spin angular momentum of $\hbar$

I know from numerous articles and also wiki (http://en.wikipedia.org/wiki/Spin_angular_momentum_of_light) that a photon carries spin angular momentum of $\hbar$. How to prove it mathematically? What ...
1
vote
0answers
67 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 ...
13
votes
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 ...
1
vote
0answers
23 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 ...
2
votes
0answers
135 views

Parke-Taylor formula in the $n=4$ simple case

I am trying to do ex. 2.23 of http://arxiv.org/abs/1308.1697. I have chosen as reference spinors $q_1,q_2 = p_3$ and $q_3,q_4 = p_1$. Therefore if I compute $A^4[1^- 2^- 3^+ 4^+]$ the computation ...
0
votes
1answer
26 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
1answer
109 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 ...
1
vote
0answers
26 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 ...
3
votes
2answers
468 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 ...
2
votes
1answer
38 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
25 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
1answer
130 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 ...
2
votes
0answers
87 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
69 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 ...
2
votes
1answer
229 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
323 views

How can neutrinos have both mass and helicity?

If a neutrino has mass it must travel at less than the speed of light. So how can it possess helicity, which can change depending on relative velocity?
0
votes
0answers
301 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 ...
0
votes
1answer
94 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
105 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
64 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
136 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
525 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 ...
1
vote
2answers
740 views

Spinor helicity formalism - original reference?

The spinor helicity formalism is a modern technique widely used in scattering amplitude calculations nowadays. However, it is hard to find a reference for who first came up with the formalism. Maybe ...
0
votes
1answer
200 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
119 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 ...
4
votes
0answers
152 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 $u^\pm$ ...
11
votes
1answer
3k 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 ...
1
vote
0answers
178 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
164 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
83 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
866 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 ...
4
votes
2answers
295 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
2answers
154 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{\...
0
votes
3answers
227 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{...