Questions tagged [diffeomorphism-invariance]
The diffeomorphism-invariance tag has no usage guidance.
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Why does diffeomorphism invariance not imply all physical theories are Poincare invariant?
It is said that diffeomorphisms are global symmetries of all theories with fixed background geometry, and local symmetry of gravitational theories i.e. theories with dynamical metric. In the case ...
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The meaning of stress tensor conservation in general relativity [duplicate]
In general relativity one has the Hilbert stress-energy tensor defined as
$$T^{\rm matter}_{ab} = -\frac{2}{\sqrt{-g}}\frac{\delta S_{\rm matter}}{\delta g^{ab}}~,$$
which is covariantly conserved i.e ...
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Resources for Faddeev-Popov method. (Specifically for diffeomorphism gauge fixing.)
I am struggling to get the same result as this paper (eq. 3.10) for my ghost field when gauge-fixing diffeomorphisms in linearized gravity. I would appreciate it if someone could point me in the ...
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In general relativity, is gauge invariance the same as coordinate invariance?
I always understood that gauge invariance of general relativity comes from the fact that the physical observables and states are the same regardless of the coordinates we choose to express them in. I ...
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How to see the diffeomorphism invariance of a particular metric
I understand how to show in general, that under the diffeomorphism $x^\mu\to x^\mu+\epsilon^\mu (x)$, the metric tensor changes as $$g'_{\mu\nu}(x')=g_{\mu\nu}(x)-\partial_\mu\epsilon_\nu(x)-\partial_\...
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Field transformation under conformal transformation
In 1 (see references below), I'm trying to derive how a spinless field transforms under a conformal transformation, specifically eq. (2.41). CFT references/lectures are the most confusing I've seen ...
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Diffeomorphisms and pullbacks
First of all, I understand that this will be mostly a mathematics questions. However, I'm asking this in the context of General Relativity, which comes with its own language, conventions and ...
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Semidirect product of Diffeomorphism group and Weyl transformations
This is more a mathematical question but in my string theory lecture we always divide in the Polyakov path integral by $$\mathrm{Diff}\ltimes \mathrm{Weyl}$$ and I was wondering why there is the ...
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Metric tensor under diffeomorphisms
It's probably a stupid question but I can't understand where I am wrong.
I have a manifold with metric $g(X,Y)$ and I know that under infinitesimal diffeomorphism ($x'^\mu = x^\mu + \varepsilon^\mu$) ...
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A Question of Pseudo-Classical Mechanics of Grassmann-Odd Variables [duplicate]
I would like to understand the following problem:
You have a classical fermion in one dimension. It has no mass, and no interactions. One can write its action as follows:
$$S=\int_{\mathbb{R}}dtL(\...
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A Question of Pseudo-Classical Mechanics of Grassmann-Odd Variables
I would like to understand the following problem:
You have a classical fermion in one dimension. It has no mass, and no interactions. One can write its action as follows:
$$S=\int_{\mathbb{R}}dtL(\...
- 2,923
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"No local gauge invariant observables in gravity"... Is it a classical or quantum statement?
I have seen different explanations to understand why there are no local gauge invariant observables in gravity.
Some of them explain that diffeomorphisms are a gauge symmetry of the theory and thus ...
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Diffeomorphism invariance for derivative of scalar fields [closed]
In GR, it is well-known that the gravitational stress-energy tensor is a pseudotensor, i.e. it is not gauge-invariant. To make it gauge-invariant one needs to take it under average integral $\langle \...
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Diffeomorphism Invariance of Terms in Lagrangian which use Gauge Fields
A term in a Lagrangian is gauge invariant if one makes sure to use quantities which transform in proper representations of the group of gauge transformations. This means that one cannot write terms ...
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Diffeomorphism invariance in 2 dimensional metric [duplicate]
I am reading "String Theory and M-Theory" by Becker, Becker and Schwarz. In Chapter 2, the authors try to gauge fix the auxiliary field. They start from the general expression
$$h_{\alpha\...
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