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

Suppose we have two coordinate systems (Cartesian and spherical) $$x^{\mu} = (t,x,y,z)$$ $$x'^{\mu'} = (t',r,\theta,\phi)$$ where $r= \sqrt{x^2 + y^2 + z^2} , \theta = \cos^{-1}(z/r), \phi = \tan^{ … asked Sep 21 '18 by Dwagg 1answer In the context of superstring compactification on a 6-manifold which admits a covariantly conserved spinor$\eta$, which we normalize so that$\eta^{\dagger} \eta = 1$, I am trying to show that the al … asked Aug 15 by Dwagg 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 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 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 …