In Nakahara's book "Geometry, Topology and Physics" in section 1.5.7 (I'm reading the second edition) he defines the functional derivative with respect to Grassmann variables. He does so in a similar way he defined that with respect to $c$-numbers, as $$ \frac{\delta F[\psi(x)]}{\delta \psi(y)} =...

Imagine a medium in which an electron is moving at speeds faster than the speed of light in the medium. Within the same medium an observer moves at the same speed with the electron. Will the observer detect Cherenkov radiation from the electron in his frame? I think the answer is no because the e...