# Questions tagged [spinors]

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### What's the equivalent of the polarization vector of photons for gravitons?

Spin-0, spin-1/2, and spin-1 particles have an associated quality expressing the spin structure of the field. Spin-0 fields obviously have no extra quality. Spin-1/2 fields are expressed by spinors ...
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### Degrees of freedom in a spinor in $d$ dimensions (following Polchinski & Lounesto)

I am working through several texts on spinors and trying to deepen my understanding of this fascinating concept. In many ways I have found Polchinski's great Appendix B of String Theory, volume 2 to ...
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### Derivation of the transformation law for spinors

I'm reading the book Quantum Field Theory: An Integrated Approach by Eduardo Fradkin, and I got stuck where the transformation law for spinors $$\psi'(x') = S(\Lambda) \psi(x)$$ is derived. In ...
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### How the factor of $1/2$ is purely conventional?

From Zee's book on group theory, he mentioned that factor $1/2$ is conventional due to historical reasons, but I thought that it was risen to match the Lie algebra of $SO(3)$? For $N=2$, the ...
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### How do you multiply a 4x1 spinor by a $SU(3)$ matrix?

I understand multiplication by a complex number, i.e. $SU(1)$ I maybe understand multiplication of the spinor by a 2x2 matrix i.e. $SU(2)$. We probably copy the 2x2 matrix twice to form a 4x4 matrix ...
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### How to dimensionally reduce the 3+1 D Dirac equation into the 1+1D Dirac equation?

In 3+1D the Dirac equation looks like $$i\partial_\mu \gamma^\mu \Psi -m\Psi=0.$$ If we only consider $x$-direction, then it should reduce to $$i\partial_t\gamma^0\Psi =(-i\partial_x\gamma^1+m)\Psi.$$ ...
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### What is the relationship between spinors and rotating motion geometrically?

Spinors are famously like spinning tops, but not actually like spinning tops since they are point particles and thus cannot rotate around their axis. It is easy to show algebraically how spinors must ...
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### Doubt on transformation laws of tensors and spinors using standard tensor calculus and group theory

1) Introduction From standard tensor calculus, here restricted to Minkowski spacetime, we learned that: A scalar field is a object that transforms as: $$\phi'(x^{\mu'}) = \phi(x^{\mu})\tag{1}$$ A ...
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### Reflection property in traces of $SU(N)$ generators

Pure gluon amplitudes could be organized on different basis, most common ones are the trace basis and the DDM (Del Duca-Dixon-Maltoni) basis, see DDM's paper, for better comprehension and to see how ...
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### Why is angular momenum related to the spin?

What I know about spin ½ particles is that they are represented by spinors, and thus, you need to apply a 720° rotation in order for the spinor to return to its original value. Spin 1 particles are ...
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### Interpretation of Feynman Slash Notation

I'm self-learning Relativistic Quantum Mechanics and was playing around with the Dirac equation when I noticed something. I was trying to interpret the meaning of ${\not} \partial$. So since I can ...
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### How to contract spinor indices?

In normal vector representation, vectors can be contracted as follows: $$v^\mu v_\mu$$ with one covariant and one contravariant index. But in spinor representation, there are 4 possible type of ...
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### Is there a completely matrix representation for the Dirac Equation?

Sorry if this question makes no sense, but I've learned that you can represent spinors as vectors, vectors as hermitian matrices, and transformation matrices as unitary operators acting on both sides ...
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### Lorentz boost property of gamma matrices

I was watching this video where he boosted the Dirac equation. He reached this equation: $$S^{-1}(\Lambda)\gamma^\mu S(\Lambda)=\Lambda^\mu{}_\nu \gamma^\nu$$ My question is since $\gamma^\mu$ is a ...
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### Charge conjugation of symplectic Majorana spinors in 4+1 dimensions

In the book "Supergravity" written by Freedman & van Proeyen, a symplectic Majorana spinor is defined in eq. (3.86) $$\chi^i = \varepsilon^{ij} (\chi^j)^C, \tag{3.86}$$ where the upper ...
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### Why does spin transform as a spinor? [duplicate]

It is often said that shortly after the binary nature of the electron spin was discovered (either plus or minus 1/2), Pauli suggested that the 2-component wave function of the electron should ...
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