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2
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0answers
19 views

Left-handed and right-handed helicity, can you explained well the phenomenon of chirality simply?

Chirality, helicity as a projection of its spin vector .. that becomes a kind of 'virtual spin'? I often confuse them: but the particles 'spin' on the right or left, or is the projection of .. what? ...
0
votes
0answers
21 views

Fierz identity in Spin(5,5) [on hold]

I am trying to understand(derive) equation 3.8 in 1208.5884 which is First, here $\gamma$ is $16\times 16$ chirally projected gamma matrices. which $\alpha=1,2,3,4,...16$ and $a=1,2,3,4,5,6,7,8,9,10$...
3
votes
1answer
37 views

Non-minimal coupling of the gauge fields to the matter

Does any one know the physical meaning of the following gauge invariant gauge coupling to the spinors? $$\bar \psi F_{\mu \nu} [\gamma^\mu, \gamma^\nu] \psi$$ This coupling is not minimal, as $$\bar \...
3
votes
1answer
21 views

What are possible ways to construct J-matrices (higher order Pauli matrices)?

I'm looking for possible ways to construct $J$-matrices. $J$-matrices are the higher-order version of Pauli matrices. Pauli matrices are suited for spin-1/2 systems, while J-matrices can be for any ...
0
votes
0answers
33 views

Basic calculus of the adjoint spinor being transformed under parity

In Modern Particle Physics (p.287) Thompson says that under the parity transformation of the adjoint spinor we have $$\bar u=u^\dagger\gamma^0\rightarrow^p (\hat Pu)^\dagger\gamma^0= u^\dagger\gamma^{...
1
vote
0answers
38 views

Acting for a covariant derivative on charged spinor [closed]

For field, theory what i know $i.e$,complex scalar QED \begin{align} D_\mu \phi = \partial_{\mu} \phi - i Q A_{\mu} \phi \end{align} and \begin{align} D_\mu \phi^{\dagger} = \partial_{\mu} \phi^{\...
1
vote
1answer
53 views

Spinors in 2+1 dimensions

I am trying to understand representations of the Poincare/Lorentz group, and in particular spinors, in 2+1 dimensions. I know some of the math, but I'm not sure about the physical interpretation of it ...
0
votes
3answers
54 views

Measuring different components of spin simultaneously

I'm reading Griffiths Introduction to QM and I'm having trouble understanding why you can't simultaneously measure the x,y and z components of spin. I know that the uncertainty principle prevents this ...
-1
votes
1answer
55 views

Real irreducible representation of $SU(2)$ [closed]

Consider a real irreducible representation of $SU(2)$ group in $d$-dimensional space-time. How many components do the spinors (eigenvectors) have? For instance, a real irreducible spinor in 10-dim has ...
0
votes
1answer
42 views

Time reversal symmetry for non-orientable manifold

From a recent paper by Kapustin(https://arxiv.org/abs/1406.7329), he argued that for non-orientable manifold with spin structure $Pin^{\pm}$, the corresponding time reversal symmetry $T$ squares to ${...
1
vote
0answers
54 views

Rotating fermion and spin structure on manifold

We know that doing a 2$\pi$ rotation would give a minus sign to wavefunctions of electrons. Since electrons are spin $1/2$ objects. How is this related to the spin structure on the manifold in which ...
0
votes
0answers
18 views

Spin half particle Magnetic field oriented along y-axis

I've been looking over past papers for an upcoming QM exam and have had a few issues wrapping my head around this question. I can follow the common example as seen in Griffiths where the field is ...
3
votes
1answer
57 views

Conceptual interpretation of the left- and right-handed spinor representations of the Lorentz group

I understand mathematically that the Lorentz group's Lie algrebra $\mathfrak{so(3,1)}$ (given by eqns. (33.11)-(33.13) in Srednicki's QFT book) is isomorphic to $\mathfrak{su(2) \times su(2)}$ (given ...
1
vote
1answer
142 views

How to find this spin wavefunction? [closed]

If an electron is in a state that the probability of measuring spin along the +x axis is $P(+x)=\dfrac{1}{2}$ and the probability of measuring spin along the +y axis is $P(+y)=\dfrac{1}{2}$, what is ...
1
vote
1answer
31 views

Anti-commutator relation of supercharges

Reading mutiple references on SUSY (e.g. Baer and Tata's Weak Scale SUSY and A SUSY Primer by S.P. Martin, arXiv:hep-ph/9709356), there seems to be different anti-commutation relation conventions for ...
4
votes
1answer
166 views

Relevance of spinor in relativistic (classical) electrodynamics

I'm following a course about relativity and electrodynamics (not the "quantum" one), and the lecture notes introduces the concept of spinor by a map between an orthogonal basis in Minkowski spacetime ...
4
votes
1answer
75 views

Schrödinger-Pauli Equation Solutions

The Schrödinger-Pauli equation is the non-relativistic limit of the Dirac equation, and therefore describes spin-1/2 particles in an external electromagnetic field. It is given by: $$\left[\frac{1}{...
5
votes
1answer
73 views

Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
0
votes
1answer
42 views

Left-handed Majorana mass term forbidden by $SU(2)$?

I'm trying to figure out why a left-handed Majorana mass term is mathematically forbidden by the $SU(2)_L$ symmetry in the context of the seesaw model. As far as I get it, it is because the left ...
1
vote
0answers
25 views

How does a linearly polarized spin 1/2 wave look like?

Spin 1 waves are easy to illustrate and a linearly polarized spin 2 wave looks like this, but what is the counterpart for a spin 1/2 wave?
0
votes
0answers
26 views

Probability density for spinors

I am approaching Relativistic Quantum Mechanics seriously for the first time, going through Bjorken & Drell and doing all the excercises, but I am facing some problems with 3.1. Derive (3.11) ...
1
vote
0answers
52 views

Fierz identity for chiral fermions [closed]

First of all I define the convention I use. The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix. I will use ...
0
votes
1answer
58 views

The true dimension of Dirac field

In natural units with $\hbar=1$ and $c=1$, as we know, the energy dimension of the Dirac field $\psi(x)$ in QED is $\frac{3}{2}$. But in cgs units, what is the true dimension of the Dirac field $\psi(...
5
votes
1answer
96 views

Spontaneous symmetry breaking of a spinor / vector field [duplicate]

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
0
votes
0answers
17 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 ...
1
vote
2answers
151 views

Deriving Pauli Matrices

How does one derive using, say, the operator formula for reflections $$ R(r) = (I - 2nn^*)(r),$$ the reflection representation of a vector $$ R(r) = R(x\hat{i} + y\hat{j} + z\hat{k}) = xR(\hat{i}) +...
2
votes
1answer
96 views

Is a Weyl fermion its own antiparticle?

Majorana fermions are their own antiparticles, and Weyl fermions are just Majorana fermions without mass. However, I haven't been able to find any source that says whether a Weyl fermion is its own ...
4
votes
1answer
171 views

Two conflicting definitions of chirality

Consider a Majorana fermion embedded in a Dirac spinor, $$\psi = \begin{pmatrix} \psi_L \\ i \sigma_2 \psi_L^* \end{pmatrix}.$$ The Majorana fermion $\psi_L$ is left-chiral, i.e. it transforms in the ...
1
vote
1answer
105 views

Deriving the Spinor Completeness Relation without using a Representation

Reference: DAMTP problem set 3, question 5 but ignore the spinor solutions given. To preface, this has taken up 1 entire day and a further 2 afternoons of work so I will just list the most promising ...
1
vote
1answer
56 views

Behaviour of Dirac Bilinears

Dirac bilinears transform in the Lorentz indices as, $\bar{\psi}\psi$ scalar $\bar{\psi}\gamma^\mu\psi$ vector $\bar{\psi}\sigma^{\mu\nu}\psi$ 2nd rank (antisymmetric) tensor $\bar{\psi}\gamma^{\mu}\...
1
vote
1answer
79 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
4
votes
2answers
84 views

Bilinears in adjoint representation

Below are two statements from my notes and I am trying to verify them explicitly. In both cases the fields are assumed to transform under the fundamental representation of $O(N)$ - --'The kinetic ...
0
votes
0answers
41 views

Confusion over trying to understand spinor components

I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
-1
votes
1answer
96 views

Gamma matrices relations (Dirac Spinors: QFT) [closed]

The entry question in an exam paper: I think I have made an elementary error in the transpose somewhere invoked by a conceptual misunderstanding of how spinors behave with gamma matrices under a ...
3
votes
1answer
88 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 ...
0
votes
1answer
56 views

When dealing with spinor indices, how exactly do we obtain the barred Pauli operator?

In the set of SUSY notes I'm following, the Pauli operator is given as: ${(\sigma^\mu)}_{\alpha\dot{\alpha}} = (I_2, \sigma^1, \sigma^2, \sigma^3)$. The antisymmetric tensor that lowers and raises ...
3
votes
0answers
90 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 ...
1
vote
1answer
68 views

Spin-1/2 with expectation values other than $\hbar/2$

I came across a problem that is related to the expectation value of spin-1/2. Assuming I want to find a single (or possibly a set of) spin state(s) $$\lvert\psi\rangle$$ that gives me an expectation ...
0
votes
0answers
22 views

Tranformation of a spinor in the self representation and conjugate representation of $SL(2,\mathbb{C})$

The transformation rules for a spinors as per Introduction to Supersymmetry by Wiedamann on Pg.38 is be summarized as: $$\begin{align} \psi_{\alpha} \mapsto \psi'_{\alpha} &= M_{\alpha}^{\beta}...
0
votes
1answer
46 views

Ordering of Contravariant and Covariant spinors. Understanding the spinor space

I've been referring to Pg.36-Pg.38 in Introduction to Supersymmetry by Wiedamann. For understanding the precise origin of dotted, undotted indices on Spinors. He starts off my saying that $M$ acts on $...
0
votes
1answer
50 views

Why are half integer and full integer spin properties of elementary particles, not of all points in space?

Tensors and spinors arise mathematically from the representation of the rotation group $SO(3)$ as a ball in 4D with all antipodal points on the surface identified. In this picture it is shown that ...
3
votes
2answers
96 views

Different definitions of spinors

Recently I've read a little about the description of particles with spin in the book Quantum Mechanics by Cohen-Tannoudji. Although I yet didn't fully study the subject, I've read one interesting part ...
1
vote
0answers
26 views

Spin-Orbit Coupling on Spherical Delta Shell

I'm trying to solve for the energy levels of a rigid rotor in the presence of spin-orbit coupling. In such a case, I'd have the Hamiltonian: $H = \frac{-\hbar^2}{2m}\nabla^2+V_0 \delta(r-a)+\frac{e^2}...
4
votes
2answers
70 views

Helicities in electron-positron annihilation

Consider the massless limit of a process in which an electron-positron pair annihilates into a virtual photon - the final state doesn't matter. If the electron is massless (or if the energy is high ...
0
votes
1answer
74 views

Gordon Identity confusion

For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, ...
0
votes
0answers
50 views

Dirac Spinors as Representation of $SL(2,\mathbb{C})$ over grassmann algebra

Recently, I've learned that the clifford algebra can be regarded as the quantization of grassmann algebra. This is shown from the following two papers by Berezin. 'Classical spin and Grassmann ...
2
votes
1answer
39 views

Weak isospin transformation of $\bar\psi \psi \phi$

In an old exam I found the following question regarding the Higgs potential: Write down the gauge invariant Yukawa interaction term in the Lagrangian that gives rise to the electron mass. The ...
1
vote
1answer
68 views

What are anticommuting spinor parameters $\zeta^\alpha$?

I'm reading Martin F.Sohnius, Introducing supersymmetry, page 82. It is the first time he introduces the anticommuting spinor parameters $\zeta^\alpha$ to calculate the supersymmetry variations of a ...
3
votes
0answers
90 views

Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
0
votes
2answers
65 views

Density matrices vs Pauli matrices

Studying quantum mechanics, I have suddenly come to the conclusion that Pauli matrices are essentially density matrices for spin systems. Does it make any sense or I have missed something?