Siyuan Ren
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 Jan22 comment Why can a circle be described by an equation but not by a function? This answer makes me realize that the question isn't so simple as it seems. Dec20 awarded Caucus Jul2 awarded Curious Mar20 awarded Popular Question Sep10 comment A question about Killing vector and Riemann curvature tensor I've left the field of math and physics and am no longer able to decipher these symbols. Sorry about your first answer. But someone else who has the same problem may one day find you answer helpful. May15 awarded Caucus Dec29 asked Is it possible to further simplify the product of three exponentials $e^A e^B e^C$ when $[A,C]=kB$ (k is a scalar) Sep14 awarded Commentator Sep14 comment Complex analysis and powers of complex values Shouldn't the second one be $\pm 1$? Since complex power to fraction is multivalued. Sep14 accepted Why is positivity of first entry sufficient for a matrix in $\mathrm{SO}(1,3)$ to be in $\mathrm{SO}^{+}(1,3)$? Sep14 awarded Yearling Sep14 awarded Editor Sep14 revised Why is positivity of first entry sufficient for a matrix in $\mathrm{SO}(1,3)$ to be in $\mathrm{SO}^{+}(1,3)$? added 27 characters in body Sep14 asked Why is positivity of first entry sufficient for a matrix in $\mathrm{SO}(1,3)$ to be in $\mathrm{SO}^{+}(1,3)$? Jun20 comment What transforms under SU(2) as a matrix under SO(3)? I stated clearly in my question: what is the equivalent transformation in SU(2) of the rotation of a linear operator (matrix) instead of vector in $\mathbb{R}^3$? Jun20 comment What transforms under SU(2) as a matrix under SO(3)? You are just re-expressing what I already know, that $\left( \boldsymbol{r}'\cdot\boldsymbol{\sigma} \right) = \boldsymbol{h} \left( \boldsymbol{r}\cdot\boldsymbol{\sigma} \right) \boldsymbol{h}^{-1}$. Jun20 comment What transforms under SU(2) as a matrix under SO(3)? @QiaochuYuan: I didn't learn the concept of "pullback". Can you elaborate? Jun20 asked What transforms under SU(2) as a matrix under SO(3)? Jun7 comment Inverse boson operator realization of $\mathfrak{so}(3)$ @QiaochuYuan: $J_{+}=a_{1}^{\dagger}a_{2},\ J_{-}=a_{1}a_{2}^{\dagger},\ J_{z}=\frac{1}{2}\left(N_{1}-N_{2}\right)$ where $a_1$ and $a_2$ are two commuting annihilation operator. Jun7 asked Inverse boson operator realization of $\mathfrak{so}(3)$