# Questions tagged [spinors]

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518 questions
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### Spinor indices manipulation in the Noether's current for free fermions

I can't solve this apparent paradox; I have the free lagrangian for massive fermions $\mathscr L = i\bar\Psi\gamma^\mu\partial_\mu\Psi - m\bar\Psi\Psi$ which is invariant under the global phase ...
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### 4-vector from a spinor

Currently reading Aitchison's book on SUSY, and on page 35 (section 2.2) he asks the reader to prove that $\bar{\Psi}\gamma^\mu\Psi=\psi^\dagger\sigma^\mu\psi+\chi^\dagger\bar{\sigma}^\mu\chi$ ...
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### Partial completeness relation for Dirac spinors

in studying trace techniques to obtain matrix elements, I came across a problem when we treat scattering of neutrinos on protons. Indeed, since those neutrinos are supposedly created in a weak decay, ...
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### How is the invariant speed of light encoded in $SL(2, \mathbb C)$?

In quantum field theory, we use the universal cover of the Lorentz group: $SL(2, \mathbb C)$, instead of $SO(3,1)$. The reason for this is, of course, that $SO(3,1)$ representations aren't able to ...
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### Interpretation of inequivalent spin structures (on the circle)

I was wondering about the physical interpretation of inequivalent spin structures on a given configuration space. For simplicity, I'd be satisified by only discussing the case of the circle. There ...
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### How to prove that Weyl spinors equations are Lorentz invariant? [duplicate]

The Dirac equation is given by: $[iγ^μ ∂_μ − m] ψ(x) = 0$ . We can prove that it's Lorentz invariant when: $ψ(x) \to S^{-1} \psi'(x')$ and $\partial_\mu \to \Lambda^\nu_\mu \partial'_\nu$, where ...
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### Why do we say that photons have spin 1 comparing with the fermoins?

I am learning QFT， and I find it very difficult to understand the spin of photon. Firstly I have some facts listed here: We can get the spin of an electron from Dirac equation. The reasons for ...
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### Which fields/particles correspond to higher dimensional representations of the Lorentz group?

To establish the Dirac equation we use Clifford algebra to find the spinor representation of the Lorentz group. A four dimensional representation tells us that the Dirac spinor describes a quantum ...
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### Solution of the Dirac equation by Pauli four-vector

Reading through David Tong lecture notes on QFT. On page 100, he solves the Dirac equation by Pauli four-vector. See below link: QFT notes by Tong, Chapter 4 In (4.107) he gives the solution in ...
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### How similar are the spin states and the matter/antimatter states?

Within the Dirac formalism, we have bispinors that represent both if a particle is spin up or spin down, and if a particle is an electron or a positron. And these representations are very similar. (...
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### If the mass of neutrino is not zero, why we cannot find right-handed neutrinos and left-handed anti-neutrinos?

I am learning P&S's Introduction of quantum field theory. My teacher said that if the mass of neutrino is exactly 0, then we should not observe any right-handed neutrinos and left-handed anti-...
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### Can Dirac equation be reformulated in an equivalent tensor form?

1) Can Dirac equation (including bispinors) be represented by a tensor formalism? 2) If yes, what kind of tensors could be the components of the wave function in Dirac equation in such formulation? ...
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