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 May 24 comment Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation @joshphysics Thanks, this is very helpful. So you're saying that $\partial_i = \frac{\partial}{\partial x^i}$ and $\partial^i = g^{ii} \frac{\partial}{\partial x^i}$ (not summing over $i$, and I guess the metric has to be diagonal)? May 24 comment Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation So Peter, you're saying the natural correspondence is, e.g.,$\frac{\partial}{\partial y} \leftrightarrow \frac{\partial}{\partial x_2}$? May 24 awarded Supporter May 24 accepted Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation May 24 comment Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation I see. Now that I think about it, we didn't actually discuss the difference between $\partial_\mu$ and $\partial^\mu$. Is the only difference a minus sign in the spatial part? May 24 asked Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation Aug 26 awarded Scholar Aug 26 accepted Why does heterodyne laser Doppler vibrometry require a modulating frequency shift? Aug 24 awarded Editor Aug 24 revised Why does heterodyne laser Doppler vibrometry require a modulating frequency shift? added 6 characters in body Aug 24 comment Why does heterodyne laser Doppler vibrometry require a modulating frequency shift? I'm not immediately making the connection to my question. Even without the modulating frequency, it is still a heterodyne technique involving the frequencies $f_0$ and $f_0+f_d$ instead of $f_0$ and $f_0+f_b+f_d$. Aug 24 awarded Student Aug 24 asked Why does heterodyne laser Doppler vibrometry require a modulating frequency shift?