# Questions tagged [dirac-matrices]

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### Derivation of the adjoint of Dirac equation

My goal is to deduce the adjoint of Dirac equation: $$\overline \psi (i\gamma^\mu \partial_\mu+m)=0 \tag{1}$$ My process: I started with Dirac equation $(i\gamma^\mu \partial_\mu-m)\psi=0$. ...
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### Could there be a pseudovector kinetic term for fermions?

Could there be a kinetic term of the form $\bar{\Psi} \gamma_5 \gamma^\mu \partial_\mu \Psi$ in addition to the usual one? Or is this forbidden by a symmetry?
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### A question about the decoupling of Dirac equation in 1+1 dimension

It is said that in 1+1 dimension, if we take $\gamma^0=i\sigma^2$ and $\gamma^1=\sigma^1$, then the two components of dirac spinor $\psi_L$(upper component) and $\psi_R$(lower component) decouple in ...
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### Mapping from spinor to tetrad

I am reading the journel by Patrick l. Nash: mapping from tetrad to Dirac spinor. While reading this ,I came across the term concrete real 4*4 irreducible representation of SO(3,3). I know SO(3) is ...
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### Gamma matrices invariant under lorentz transformation

I know this has been asked before but I just can't seem to get my head around it based on the answers I've read. So the idea is that we have the gamma matrices $\gamma^{\mu}$. Now from my ...
1answer
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### weak interaction are not parity invariant

I'm having some hard time trying to see why the left-handed lagrangian for fermions $\psi$, $$\mathcal{L} := G\overline{\psi}_{1L}\gamma^\mu\psi_{2L}\overline{\psi}_{3L}\gamma_\mu\psi_{4L}$$ is not ...
1answer
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### How to prove $\{\gamma^{\mu}, \gamma^{\nu}\}$ ? (notation problem)

I want to prove that $\{\gamma^{\mu}, \gamma^{\nu} \}=2g^{\mu \nu}$ what are the indices $\mu$ and $\nu$ here? because I know the gamma matrices from 0 to 5 and I need to verify the anti ...
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### Question about $\gamma^{0}$ matrix

I see different definitions in different places so here is my question. why is $\gamma^{0}$ sometimes defined as a 2 by 2 matrix and sometimes as a 4 by 4 matrix? shouldn't a definition be something ...
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### About the central charge of 4D extended supersymmetry algebra

The 4D SUSY algebra can be written as $$\{ Q_{\alpha}^{A} , Q_{\beta}^{B \dagger} \} = 2 m \delta^{AB} \delta_{\alpha \beta} + 2 i Z^{AB} \Gamma^0_{\alpha \beta}, \tag{B.2.37}$$ in a particular ...
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### Derivative of an Expression with respect to One Component of Strain

I recently come across a paper in which the notation of some equation confuses me a lot. Let's say, if I have an expression represented by delta $\delta_{jk},\delta_{jl}$, infinitesimal strain tensor \$...