# Tag Info

## Hot answers tagged differential-geometry

### Showing that a generator exponentiates to a $\mathbb{R}$ group

From now on $\{\cdot,\cdot\}$ denotes the Lie commutator of smooth vector fields on a smooth manifold. As far as I understand, you have a vector field $X$ on $TM$, where $M$ is the Schwarzschild ...
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### Derivation or origin of projection tensor

Take an arbitrary vector $X^a$. Its projection along $u^a$ direction will be $X^bu_b u^a$. Then the component orthogonal to $u^a$ will be simply $X^a-X^bu_bu^a = (\delta^a_b - u_bu^a)X^b={P^a}_bX^b$
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Accepted

### Chose coordinates where $g_{01}=g_{02}=g_{03}=0$ to disentangle space and time?

Yes of course you can do that. You can even go beyond to impose $g_{00}=-1$. This is thank to the coordinate freedom which lets you fix 4 out of 10 metric components. Then you are remained with ...
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### On the Background Independence condition

This could sound counterintuitive but the background independence condition means that the dynamics of a field depend on the background. I am gonna explain myself: Classical Field Theory Assume we ...
• 1,809

### Understand the Lorentz transformation in QFT

I want to propose a different approach, as I believe the OP might benefit from comparing different viewpoints on distribution theory. The question is really about the transformation of distributions ...
• 36.7k
1 vote

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1 vote
Accepted

### Understanding and Expressing the Definition of Inertia Tensor in the Language of Differential Geometry

\$\newcommand{\R}{\mathbb{R}} \newcommand{\E}{\mathcal{E}} \renewcommand{\O}{\mathrm{O}} \newcommand{\SO}{\mathrm{SO}} \newcommand{\so}{\mathfrak{so}} \renewcommand{\d}{\mathrm{d}} \renewcommand{\r}{\...
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