# Questions tagged [dirac-matrices]

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### Contracting gamma matrices with explicit indices

So I was calulating the matrix element of an interaction and arrived at the following contraction $$\gamma^\mu_{ab}\gamma_{\mu\,cd}$$ With $a,b,c,d$ spinor indices that are never contracted with ...
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### Spinorial representation of Lorentz group for solution to Dirac equation

In my relativistic quantum mechanics course, we found plane wave solution to the Dirac equation by first studying it the reference frame of the particle. Using a plane wave solution for both positive ...
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### Relativistic quantum field theory

Let $\psi(x)$ be solution of Dirac equation $$(\gamma^\mu\Pi_\mu-mc) \psi(x)=0$$ where $\Pi_\mu=i\partial_\mu-eA_\mu$ is momentum operator in present electromagnetic field . We consider tow ...
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### Spin for Dirac fermions proof $\Sigma_{i}=\frac{1}{2} \gamma_{5} \gamma_{0} \gamma_{i}$

The spin for Dirac fermions is defined as: $$\Sigma_{i} \equiv \frac{1}{4}\epsilon_{ijk}\sigma_{jk}$$ Without using an explicit representation for the matrices, I would like to show that the spin ...
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### Proving an identity relating the gamma matrices

I'm looking to prove the following identity: $$k_a \gamma^a \gamma^\nu K_b \gamma^b p_c \gamma^c \gamma_\nu P_d \gamma^d = 4(p\cdot K)(P\cdot k)$$ I tried this many times but always seem to be stuck ...
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### Physics Meaning of Trace Technology in QED [closed]

As it pointed out on page 133 of Peskin and Schroeder, any QED amplitude involving external fermions, when squared and summed or averaged over spins, can be converted to traces of products of Dirac ...
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### What do the matrices $\alpha_k$ represent in the Dirac equation?
I have been scouring the internet for an answer. All I have managed to find are the matrices for $k=1,2,3,4,5$. However, I still have no idea they represent, within the equation. Am I correct in ...