# Tagged Questions

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

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### Does curved spacetime change the volume of the space?

Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
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### What is the minimum math level required to comprehend general relativity? [duplicate]

I am currently working on a B.S. In chemistry and only need to go up to Calculus II, though I like to dabble in physics. What other math classes could I take to gain greater understanding of higher ...
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### How can I mathematically describe the parallel transport in the Roman soldiers example?

I've been trying to understand parallel transport. Many of the descriptions present a mathematical version: $\nabla_V X = 0$. And/or they present an example involving soldiers (usually Roman) ...
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### A question on the Chern number and the winding number?

Let $\mid \psi(x,y) \rangle$ be a normalized wavefunction living in a $d$-dimensional Hilbert space and depend on two real parameters $(x,y)$ that belong to a closed surface (e.g., $S^2, T^2$, ...). ...
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### Interesting Hamiltonian System [duplicate]

The definition of a Hamiltonian system I am working with is a triple $(X,\omega, H)$ where $(X,\omega)$ is a symplectic manifold and $H\in C^\infty(X)$ is the Hamiltonian function. I am wondering if ...
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### Stokes' theorem in complex coordinates (CFT)

I am studying CFT, where I encounter Stokes' theorem in complex coordinates: $$\int_R (\partial_zv^z + \partial_{\bar{z}}v^{\bar{z}})dzd\bar{z} = i \int_{\partial R}(v^{z}d\bar{z} - v^{\bar{z}}dz).$$...
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### How can I show that inversion is continuously connected to a reflection?

From Ex 3.1 in the TASI lectures on the conformal bootstrap: http://arxiv.org/abs/1602.07982 the problem is the inversion map (with Euclidean signature) $$I\colon x^\mu \mapsto \frac{x^\mu}{x^2}$$ ...
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### Rotating fermion and spin structure on manifold

We know that doing a 2$\pi$ rotation would give a minus sign to wavefunctions of electrons. Since electrons are spin $1/2$ objects. How is this related to the spin structure on the manifold in which ...
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### General relativity applications other than gravity

Do the Einstein field equations successfully predict/describe physical processes other than gravitational ones?