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 13h answered A question about the Fermi acceleration 16h comment Dipole moment of a single point charge If the moments up to order $n-1$ vanish, the moment of order $n$ is independent of coordinate system. Perhaps you should add "in general" to the first sentence? 1d comment Converting between matrix multiplication and tensor contraction @tfb Some months ago I came across this, which reminds me of your story. 1d comment Unitary operators evolving the set of Pauli matrices The paper mixes two conventions and probably defines $\vec{\sigma}(t) = \sigma_1(t) \vec{e}_1 + \sigma_2(t) \vec{e}_2 + \sigma_3(t) \vec{e}_3$, where the vector space is defined by the Pauli matrices, i.e. $\vec{e}_1 = \sigma_x$, etc. 1d comment Unitary operators evolving the set of Pauli matrices Check Frobenius's answer below, it's more explicit. Does the paper define $\vec{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$? 1d comment Unitary operators evolving the set of Pauli matrices For example, $\vec{\sigma}_{11}$ is $\vec{e}_z$. Probably, the notation confuses you because you interpret $\vec{e}_i$ in terms of coordinates. Vectors are elements of a vector space and it is an extra step to assign coordinates to them. The vector spaces where $\vec{e}_i$ and $\sigma_{i}$ belong are not the same in general! 1d comment Unitary operators evolving the set of Pauli matrices $\sigma_{ij}$ is the $i,j$-th element of the matrix $\vec{\sigma}$. A common convention is to interpret $i$ as the row and $j$ as the column. 1d comment Unitary operators evolving the set of Pauli matrices This notation can be used even if the coefficient matrices are linearly dependent! 1d comment Unitary operators evolving the set of Pauli matrices $\vec{\sigma}$ is a $2\times 2$ matrix, $\sigma_x \vec{e}_x + \sigma_y \vec{e}_y + \sigma_z \vec{e}_z$. 2d answered Is the electric field of a volume charge distribution well defined? Apr 10 awarded Student Mar 22 awarded Enlightened Mar 22 awarded Nice Answer Dec 14 answered Ernst potential from Kaluza-Klein reduction of axisymmetric space-time Nov 23 awarded Yearling Nov 15 comment Why do we obtain classical physics by taking the limit of Planck's constant to zero? Well, one obvious reason is that $h$ does not appear in the equations of classical physics. If $[x,p]=0$, every state is defined simultaneously by position and momentum, which differentiates between the classical and the quantum theory. This answer does not explain certain details, which appear in chapter VI, §1 of Quantum mechanics by Messiah. Nov 13 comment Conservation of energy and Killing-field Also, it is not necessary that the Killing vector is timelike, it is necessary that it is asymptotically timelike, and this is for the reason described in my answer below, namely that the scalar defined using it has the appropriate asymptotic behaviour. In Kerr space-time, $K^a$ may be space-like! Nov 13 comment Conservation of energy and Killing-field "Physically, asymptotically flat space-times represent isolated systems", cf. Robert Geroch and Jeffrey Winicour. Linkages in general relativity. Journal of Mathematical Physics, 22(4):803-812, 1981. Nov 13 revised Conservation of energy and Killing-field Probably used the wrong word "for" instead of "in". The former might confuse someone in that the answer refers to the energy of the spacetime. Nov 12 answered Curvature of Conical spacetime