# Questions tagged [diffeomorphism-invariance]

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### How does the renormalization process differ between actions with and without diffeomorphism invariance?

If I have an action that is not invariant under a change of coordinates. Does this effect the renormalizability of the theory? The procedure of renormalizing a field theory essentially boils down to ...
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### Does the action have to be coordinate invariant?

Is the Lagrangian density $\mathcal{L}$ in the action $S=\int d^4x \sqrt{-g}\mathcal{L}$ required to be coordinate independent? If so, and a set of EOM are not invariant under coordinate ...
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### What special symmetries is this subset of diffeomorphisms?

To make a general diffeomorphism I can make an infinitessimal transformation to the coordiante $x^\mu$ to $x^\mu + \delta f^\mu(x)$. Now I want to restrict it so I only allow transformations such that:... 1 vote
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### Proof of volume density transformation under infinitesimal diffeomorphisms using Levi-civita/ determinant

Given I diffeomorphism $x^\mu \rightarrow y^\mu = y^\mu(x)$, I want to show that the volume density is invariant, i.e. $\sqrt{-g(x)}\,\mathrm d^4x \rightarrow \sqrt{-g(y)}\,\mathrm d^4y$. The ...
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### Understanding the metric transformation under infinitesimal diffeomorphism

In my general relativity course, we are discussing infinitesimal diffeomorphisms defined by $x^{\mu}\rightarrow y^{\mu}(x) = x^{\mu} + \xi^{\mu}(x)$. We have been examining how different objects ...
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### Weyl transformation vs diffeomorphism; conformal invariant vs general in/covariant

Background info: My understanding: 1. Weyl transformation is a local rescaling of the metric tensor $$g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}$$ A theory invariant under this Weyl transformation is ...
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