# Questions tagged [spinors]

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### Trying to understand spin

My question is fairly simple and straightforward. I'm studying Quantum Mechanics, specifically the spinor formalism. I understand that one can define a generator of rotations, say around axis $z$ by ...
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### Accounts on the solutions of the Dirac equation

Consider the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi = 0$. As it is well known, there are different representations for the matrices $\gamma^{\mu}$, $\mu = 0,1,2,3$, the most famous ones ...
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### What is Dirac indices?

In Maggiore A Modern Introduction to Quantum Field Theory Eq. 4.31 $$\{\Psi_a(\vec x,t),\Psi_b(\vec x,t)\}=\delta^{(3)}(\vec x-\vec y)) \delta_{ab}$$ where "$a,b=1,2,3,4$ are the Dirac ...
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### Problem with constructing a bispinor in the spinor helicity formalism

The $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group is constructed as $(\frac{1}{2},0) \otimes (0,\frac{1}{2})$. To get an element of the vector space this specific representation acts ...
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### Under which representation (and how exactly) transforms the given bispinor? [duplicate]

I am currently reading through Chapter 27 (Spinor helicity formalism) in Schwartz´s "QFT and the SM". In this chapter it says that since 4-momenta transform in the (1/2,1/2) representation ...
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### Weyl Spinor Representation and Single Particle States

I'm trying to study representation theory for quantum field theory. Let me first summarize my current state of (hopefully correct, please correct me if I'm wrong about something) knowledge: Single ...
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### Standard model notation on doublets

$\require{cancel}$ I have been introduced to electroweak theory in lectures and I wanted to check I understand the notation for the doublets, triplets etc. Take the first generation lepton left handed ...
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### Lorentz boost of Dirac spinor

Let $\psi_\vec{0}^+$ be a Dirac wavefunction describing a motionless particle, $$\psi_\vec{0}^+(x) = \sqrt{2m} \begin{pmatrix} \chi \\ 0 \end{pmatrix} e^{ip \cdot x}$$ where $p = (m, \vec{0})$. ...
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### Charge conjugation on spinors: Am I missing a (-1)? [duplicate]

I'm trying to prove the transformation rules for Dirac Bilinears under charge conjugation as given in "Fundamentals of neutrino physics and astrohysics" by Carlo Giunti et.al. According to ...
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### How to describe a time dependent spin state from initial state?

If i have the initial spin state defined like this: Of which has an applied magnetic field along some axis say the $z$-direction. How do you then define $A$ with time dependence and what axis are the ...
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### Weyl spinor being on-mass or off-mass shell

Is there a way to know whether a two component Weyl spinor is on-mass or off-mass shell?
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### Bhabha scattering in the spinor-helicity formalism

I am trying to calculate the square amplitude for Bhabha scattering $e^-(p_1)e^+(p_2)\rightarrow e^-(p_3)e^+(p_4)$ using the spinor-helicity formalism but one of the interference terms just will not ...
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### Rotation operator from angular momentum or spin operator

My instructor on quantum physics just stated that the total angular momentum operator, $\hat{J}$, can be expressed as $\hat{J}=\hat{L}+\hat{S}$, where $\hat{L}$ is angular momentum operator ...
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### What are the Feynman rules for the spinor-helicity formalism?

If we do not work with helicity amplitudes, there are Feynman rules for the external legs of a Feynman diagram, i.e. $u_s(k),\overline{v}_s(k),\epsilon_r(k)$ for an incoming fermion, antifermion and ...
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### Does Wightman's unitary $U(\Lambda)$ really exist for Lorentz boost?

This question is related to another question here. But I am asking a more fundamental question about the existence of Wightman's unitary $U(\Lambda)$ for Lorentz transformation. Let $\psi^\alpha$ be a ...
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### What do these matrices represent physically? Are they related to Majorana spinors?

I am studying $\mathfrak{so}(1,3)$ representations and I found this claim that $(m,n)\oplus(n,m)$ representations have a real structure (for which I asked a separate question on math.SE). I tried to ...
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### Spatial inversion and Time reversal

On the spinor field $\psi^{\mu}(x)$, I found the action of $\psi^{\mu}(x)$ on spatial inversion $P$ by postulating $\psi^{\mu}_{P}(x)=P^{\mu}_{\nu}\psi^{\nu}(P^{-1}x)=P^{\mu}_{\nu}\psi^{\nu}(t,-x)$, ...
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### Does this argument prove that all fermionic states have zero norm?

The following argument seems to show that all states created by a fermionic field have zero norm. This would surely cause problems in QFT, so I believe there must be an error somewhere, but I can't ...
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### An essential exercise involving spin composition

Suppose we have two particles with spin $1/2$. They have $S^{tot}=1$ and $S^{tot}_y=0$. How can we write the state of the system in terms of the eigenstates of $S_{1z},S_{2z}$? My attempt: I would ...
While reading an article, it's said that to simplify the following Dirac structure $$\left(P_Lv_j^d\bar{v}^s_kP_R\right)_{\alpha\beta}\tag{1}\label{1}$$ where $j,k$ are color indices and $d,s$ ...
The (covariant) vector transformation law is given by: $$V^{'}_{\mu} = t^{\nu}\hspace{0.1mm}_{\mu'}V_{\nu} =\frac{\partial x^{\nu}}{\partial x'^{\mu}}V_{\nu} \tag{1}$$ where the transformation is ...