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Mathematical discipline which uses the techniques of calculus to study geometric problems. General relativity is written in this language.

1
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2answers
Suppose we have two coordinate systems (Cartesian and spherical) $$x^{\mu} = (t,x,y,z)$$ $$x'^{\mu'} = (t',r,\theta,\phi)$$ where $r= \sqrt{x^2 + y^2 + z^2} , \theta = \cos^{-1}(z/r), \phi = \tan^{ …
asked Sep 21 '18 by Dwagg
2
votes
1answer
In the context of superstring compactification on a 6-manifold which admits a covariantly conserved spinor $\eta$, which we normalize so that $\eta^{\dagger} \eta = 1$, I am trying to show that the al …
asked Aug 15 by Dwagg
2
votes
2answers
I've seen the Yang-Mills Bianchi identity written as both $$0 = dF^a + f^{abc} A^b \wedge F^c$$ and, in tensor notation, as $$\epsilon^{\mu\nu\lambda\sigma}D_{\nu} F^a_{\lambda\sigma} = 0.$$ Here …
asked Aug 11 by Dwagg
7
votes
1answer
For instance in Blumenhagen's CFT, there is a standard argument which determines that globally defined conformal transformations on the Riemann sphere where $$l_n = -z^{n+1} \partial_z$$ is …
asked Dec 19 '18 by Dwagg
6
votes
1answer
Although I've forgotten the proof (and cannot find it in, say, Carroll's book), the following formula holds for the covariant divergence in general relativity: $$\nabla_{\mu} A^{\mu} = \frac{1}{\sqrt …
asked Oct 1 '18 by Dwagg