# Tagged Questions

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### Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
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### $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus (0,\frac{1}{2})$ [duplicate]

I am confused about the notation. What's the differences between $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus (0,\frac{1}{2})$, or maybe $(\frac{1}{2},0)\bigoplus (\frac{1}{2},0)$ ? (...
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### What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
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### Generalization of De Rham cohomology for spinor fields

I am interested in possible generalizations of The De Rham cohomology for spinor fields. I am also interested in applications to physics such as in the construction of topological charges I can see ...
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### How to construct the charge conjugation matrix for any given dimension?

Generally, Gamma matrices could be constructed based on the Clifford algebra. $$\gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij},$$ My question is how to generally ...
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### Twistor notation in space-time (Part 1)

This is sort of a continuation of this and this previous discussions. In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real ...
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### Spinor integration

I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is explained....
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### How does the Lorentz group act on a 4-vector in the spinor-helicity formalism $p_{\alpha\dot{\alpha}}$?
Given a 4-vector $p^\mu$ the Lorentz group acts on it in the vector representation: $$\tag{1} p^\mu \longrightarrow (J_V[\Lambda])^\mu_{\,\,\nu} p^\nu\equiv \Lambda^\mu_{\,\,\nu} p^\nu.$$ However, I ...
The covariant form of the Dirac equation is given by $$(i\gamma^{\mu}\partial_{\mu} - M) \Psi(x) = 0$$ Einstein's summation is implied here, $x=(x^0,x^1,x^2,x^3)^T$. I am simply looking for the ...