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How to derive this form of helicity spinor (massless/high energy limit)

First there is an intuitive explaination, for Dirac fermions, the mass term is \begin{align*} \left(i\partial_{\mu}\gamma^{\mu}-m\right)\Psi & =0\\ \Psi & =\begin{pmatrix}\psi_{L\alpha}\\ \...
Yakumo Ran's user avatar
4 votes
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Different representations of the Yukawa interaction

Your second expression is meaningless. You need to saturate a row vector with a column vector, not to mention the spinor implicit index saturation, so it should be, instead, $$y_e \bar{e}_R H^\dagger ...
Cosmas Zachos's user avatar
2 votes

How to rotate an electron mathematically?

The simple answer is that physical rotations are continuous, so they can be described not by a point in $SO(3)$ or $SU(2)$ but by a path from the origin. Such paths are unambiguous since $SO(3)$ and $...
benrg's user avatar
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1 vote
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Question about meaning of "bar"-ing in the context of Dirac fields

I.e, is $$\begin{pmatrix} A & B \\ C & D \end{pmatrix}^\dagger =\begin{pmatrix} A^* & C^* \\ B^* & D^* \end{pmatrix}$$ where $A,B,C,D$ are 2 by 2 matrices. Or $$\begin{pmatrix} A & ...
hft's user avatar
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3 votes

How to rotate an electron mathematically?

The other answers in this post invoking "quantum mechanics" or "quantum states" to explain the classical spinor behavior are totally misguided. When the great mathematician √Člie ...
MadMax's user avatar
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How to rotate an electron mathematically?

(I wrote this answer in a hurry yesterday, I now fixed a huge number of typos and various mistakes, sorry.) Well, there are a number of important issues in the question. First of all, pure quantum ...
Valter Moretti's user avatar
8 votes

How to rotate an electron mathematically?

This experiment has actually been done with neutrons. The first publication is Werner et al., PRL 35, 1053 (1975). The experiment was done with a neutron interferometer. A low-intensity beam of ...
rob's user avatar
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The physical (classical) significance of the spinor representation of an electron

Can we assign a physical (classical / correspondence principle) interpretation to the double rotation (720 degrees) required to describe electrons? It's a wrong question to ask "why double ...
MadMax's user avatar
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The physical (classical) significance of the spinor representation of an electron

Can we assign a physical (classical / correspondence principle) interpretation to the double rotation (720 degrees) required to describe electrons? Possibly. Here is a metaphor, something else which ...
J Thomas's user avatar
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1 vote
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Product of spinors in Dirac field anticommutators

You have to use the relations $$ \sum\limits_s u_a^s(p) \bar{u}_b^s(p) =(p \! \! \! /+m \, \mathbb{I})_{ab} \quad \text{and} \quad \sum\limits_s v_a^s(p) \bar{v}_b^s(p) = (p \! \! \! /-m \, \mathbb{I})...
Hyperon's user avatar
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Quark Combination of Hadrons

You are confusing two different things: If you see the notation $\pi^+ = u \bar{d}$ (e.g. in the Particle Data Tables), this simply means that the quark content of a charged pion is given by an up-...
Hyperon's user avatar
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Fierz idendity (supersymmetry)

We define \begin{align} \psi \chi &\equiv \psi_a \chi^a = - \epsilon_{ab} \psi^a \chi^b , \qquad {\bar \psi} {\bar \chi} \equiv {\bar \psi}^{\dot a} {\bar \chi}_{\dot a} = \epsilon_{{\dot a}{\dot ...
Prahar's user avatar
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