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-3
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0answers
34 views

Pauli Spin Matrices [on hold]

i) Determine the effect of the pauli spin matrices $\sigma_x$ and $\sigma_y$ on the eigenstates of $\sigma_z$. Which physical process is conveyed on the eigenstates of $\sigma_z$ by applying ...
1
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0answers
24 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
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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
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0answers
41 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
51 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 ...
5
votes
1answer
85 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
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0answers
12 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
0answers
44 views

Deriving Pauli Matrices

How does one derive using, say, the operator formula for reflections $$ R(r) = (I - nn^*)(r),$$ the reflection representation of a vector $$ R(r) = R(x\hat{i} + y\hat{j} + z\hat{k}) = xR(\hat{i}) + ...
2
votes
1answer
76 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
161 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
79 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
50 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 ...
1
vote
1answer
74 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 & ...
3
votes
2answers
77 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
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0answers
38 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
90 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
65 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
53 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
71 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
63 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} &= ...
0
votes
1answer
42 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
45 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
90 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
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0answers
24 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 ...
4
votes
2answers
60 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
57 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
43 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
34 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
64 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
88 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
55 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?
2
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0answers
98 views

Supercovariant Derivative action

My query is with Weinberg Vol3 equation just above 26.7.22 Weinberg follows Majorana Superfield formalism. Where, covariant derivative is defined as, $$D_{R\alpha}=-\epsilon_{\alpha ...
2
votes
2answers
89 views

Why can the spin of a relativistic particle not be orthogonal to its momentum?

I have read that the 3-momentum of a relativistic particle cannot be orthogonal to its spin 3-vector. When thinking about how the spin vector transforms when the particle approaches light speed, it ...
0
votes
1answer
90 views

Geometry of spacetime and spinor bilinears

In this paper (http://arxiv.org/abs/0704.0247) p.20, the author says in the section titled Geometry of spacetime the following: In order to obtain the spacetime geometry, we consider the spinor ...
1
vote
1answer
61 views

How do we know if a Killing Spinor is Time-like or Null?

How to know whether a Killing spinor orbit is time-like or null? This is present in a paper like this 29/39 here. I'm not asking for a technical answer, just a logical cliche answer chit-chat answer. ...
0
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0answers
33 views

Basic Dirac Spinors question

Here p. 25, it says Generically, the space of Dirac spinors has $2^{d/2}$ (complex) components, and one can recast them in terms of the complexified space of forms on $\mathbb{R}^{d/2}$. My ...
1
vote
1answer
51 views

Why do $\psi_a$ and $\bar{\psi}_{\dot{\alpha}}$ represent two different degrees of freedom?

I am taking a course in QFT and I've been introduced to the concept of left-handed (undotted) and right-handed spinors (dotted). I know that left-handed spinors are associated with the irreducible ...
0
votes
1answer
101 views

What are susy transformations for N=2 sugra?

Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories. As suggested by some books and papers on ...
0
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0answers
48 views

Spin-1/2 rotation operator: rotation about an angle of $\pi$

The spin-1/2 rotation operator: $$ R_{n}(\alpha) = \begin{pmatrix} cos(\frac{\alpha}{2})-in_{z}sin(\frac{\alpha}{2}) & (-in_{x}-n_{y})sin(\frac{\alpha}{2}) \\ ...
0
votes
1answer
52 views

spin representations and polynomials

I'm reading Group Theory and General Relativity by Moshe Carmeli and his discussion of spin representations of SU(2) and the isomorphism to the space of homogenous polynomials is confusing me. I'll ...
0
votes
0answers
59 views

Solving Weyl Equations

In my second taking of QFT we just finished the Dirac equation. As an exercise I tried applying what I have (re-) learned to the Weyl equations. I'd like someone to check if my work is correct. For ...
5
votes
0answers
60 views

$(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus (0,\frac{1}{2})$ [duplicate]

I am confused about the notation. What's the differences between $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus (0,\frac{1}{2})$, or maybe $(\frac{1}{2},0)\bigoplus (\frac{1}{2},0)$ ? ...
1
vote
0answers
45 views

How can we use Majorana spinors for charged fermions in MSSM?

According to "Supersymmetry in Particle Physics" by Ian Aitchison (see e.g. p62 of arXiv), in the Minimal Supersymmetric Standard Model (MSSM) we can use Majorana language to build supermultiplets: ...
0
votes
2answers
27 views

Which particles have helicity?

I know electrons have helicity but can particles which are not fundamental i.e.protons have helicity?
0
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2answers
46 views

Pseudoscalar current of Majorana fields

Consider a Majorana spinor $$ \Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right) $$ and an pseudoscalar current $\bar\Phi\gamma^5\Phi$. This term is invariant under hermitian ...
2
votes
1answer
34 views

Helicity amplitudes and muon/electron currents

I have the following helicity spinor: $$ u_R=\sqrt{E} \begin{pmatrix} c \\ se^{i\phi} \\ c \\ se^{i\phi} \end{pmatrix} $$ We take $s=\sin\theta/2$ and $c=\cos\theta/2$. Also, $E$ and $\phi$ are ...
0
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0answers
46 views

Cyclicity of trace with fermionic arguments

I think this is a non-question, but it has me considerably worried. Consider the piece of a Lagrangian density given by, $$\mathcal{L} = ...
2
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0answers
67 views

Tensor product of spin states

I just wanted to check that I carried out this problem correctly. I got the correct answer, but I'm not sure if what I did to get it is completely correct. This is from the second part of problem 3.4 ...
1
vote
3answers
95 views

Why is this proof that all $\overline{\psi}\psi\overline{\psi}\psi$ interactions are trivial incorrect?

This is a homework question for my quantum field theory class. I haven't been able to figure out the answer, and neither has anybody I asked. The homework was due two days ago. Consider a spinor ...