josh
Reputation
521
Top tag
Next privilege 1,000 Rep.
Create tags
 Feb22 awarded Yearling Aug28 comment Help with spinor indices Are you sure the Kronecker $\delta$ is not invariant? Tell me in which frame it has the usual 0 and 1 components, then. What does it look like in another frame? Aug27 comment Help with spinor indices Another way to think about all of this is to use the Lie algebra isomorphism ${\rm so}(4) \simeq {\rm su}(2) \times {\rm su}(2)$ and $\alpha$ as the index on $(1/2,0)$, $\dot\alpha$ on $(0,1/2)$ and $\mu$ on $(1/2,1/2)$. Then $\sigma^\mu{}_{\alpha\dot\alpha}$ projects $(1/2,1/2) \times (1/2,0) \times (0,1/2)$ onto the trivial representation $(0,0)$. Aug27 comment Help with spinor indices Try it in two parts: first you know that $\varepsilon^{\alpha\beta}$ is an invariant tensor (which is why it's admissible to use it to lower and raise indices in a meaningful way). You've given the components for $\varepsilon^{\alpha\beta}$ and $\varepsilon_{\alpha\beta}$. How about $\varepsilon^\alpha{}_\beta$? Once you have that, why not use $\varepsilon$ to raise the $\alpha$ on both sides of your final equation? Aug27 comment Construct a sample space $\Omega$ What have you tried? Aug26 comment Paradoxes without self-reference? The subject of "it" is the quotation, i.e. the subject of that sentence. The sentence is not the quotation, that's the point. If the subject had been "this sentence", e.g., then the sentence would have been self-referencing. This is an important distinction: not every use of the word it replaces "this sentence," including in Quine's famous example above. Aug25 answered Paradoxes without self-reference? Aug25 awarded Commentator Aug25 comment Find CFG for Lisp-like expressions The computer science stack exchange may get you better results. There are two of them: cs.stackexchange.com and cstheory.stackexchange.com Aug24 comment Issue with a Poisson process and its jump times Try working recursively. Can you say what is the distribution of $(T_1,T_2)|{N_t = 2}$? Jun5 answered derivative of exponential of matrix trace Jun5 comment derivative of exponential of matrix trace You need to clarify your notation a bit. Is $C_{ij}$ a constant matrix for each pair $ij$, i.e. a family of matrices labeled by two indices, $i$ and $j$, or is $C$ a matrix with components $C_{ij}$? If the latter, then there is no additional summation over $i$ and $j$ after evaluating $e^{-{\rm tr}(X^T C X)}$. Jun5 answered Green's theorem and flux Apr2 comment Determinant of the transpose of elementary matrices no big deal, glad you understand more now too. Mar20 comment Determinant of the transpose of elementary matrices It is not true that $\det{M} = \mathrm{tr}\,M$ for upper or lower triangular matrices. Feb22 awarded Yearling Nov5 revised How many integer solutions to a linear combination, with restrictions? deleted 5 characters in body Nov5 answered How many integer solutions to a linear combination, with restrictions? Apr1 answered Old MIT exam question, how do I solve it? Mar14 suggested rejected edit on Newton-Raphson's Method to find $\sqrt{2012}$