# Tagged Questions

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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Local Lorentz transformations

If $\gamma^m$ denotes a tangent space gamma matrix, and $\gamma^\mu$ denotes a curved space gamma matrix, then they are related by $$\gamma^\mu(x) = \gamma^m e_{m}^{\mu}(x)$$ where $e_{m}^{\mu}(x)$ ...
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### Are fermions intrinsically non-local?

Background: When one studies quantum mechanics of more than one particle, one learns that all fundamental particles can be classified as either bosonic or fermionic. Fermions have a spinor structure, ...
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### Conformal compactification and the use of spinors (Twistor theory)

I was reading the book from Huggett and Tod "An introduction to twistor theory" and as the book evolves they reach to the necessity to "found" a Lie derivative of a spinor respect to a conformal ...
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### Twistor theory. Huggett and Tod (problems with one equation)

I'm reading about twistors from the book of Huggett and Tod: $\textit{ An introduction to twistor theory}$. I'm trying to understand everything and reproduce every equation that comes here. So, ...
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### Spinor field normalisation from poles in the propagator

In the theory of free scalar bosons (KG field) it is a basic result that the propagator $\Delta(p)$ has poles at $p^2=m^2$, with residue $1$ (or any other constant, depending on conventions). Thinking ...
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### Index Placement for Spinors in Relativity

This may ultimately be a silly question, but a pedantic mind like mine gets tied into knots over differing notation. (Disclaimer: I'm a mathematician.) Let $\mathbb{W}$ be a complex two-dimensional ...
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### Derivation of Dirac equation in curved spacetime

In all the Literature I have read, the covariant Dirac equation in curved spacetime is given as \left(i\hbar\gamma^{\mu}(x)\left[\frac{\partial}{{\partial}x^{\mu}}-{\Gamma}_{\mu}(x)...
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### Four-momentum and Dirac equation in curved spacetime

Norm of four momentum in Minkowski spacetime is proportional to the square of rest mass as $$|P|^2= P^\alpha \eta_{\alpha\beta}P^\beta= (E/c)^2 - p^2 = (mc)^2$$ While in ...
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### Spin 1/2 wavefunction transformation under inversion and mirror symmetry

I'm considering group-theory applications to condensed matter physics now. In particular I work with the following paper: http://journals.aps.org/pr/pdf/10.1103/PhysRev.100.580 and try to understand ...
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### Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
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### Do the eigenstates of the Pauli operators correspond to the six directions of the 3D world?

I understand that the six eigenstates of the three Pauli operators $X, Y, Z$ correspond to the six poles of the Bloch sphere. By fixing an orthonormal basis of our physical word, does "measuring Pauli ...
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### Covariant derivative commutator on spinors [closed]

What is this object $[\nabla_{\mu},\nabla_{\nu}]\epsilon$ in terms of curvature tensor $R_{\mu\nu}$? Where $\nabla_{\mu}$ is the covariant derivative on a four sphere and $\epsilon$ is spinor. PS: I ...
I am trying to prove the Lorentz invariance of the (left-handed) Weyl Lagrangian: $$\mathcal L=i\psi^\dagger\bar\sigma^\mu\partial_\mu\psi$$ A Lorentz transformation is realized as $\psi\to M\psi$, ...