# Questions tagged [diffeomorphism-invariance]

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### Diffeomorphism invariance and energy momentum conservation

I was reading Sean Carroll book "Space-Time and geometry", in the appendix B he derives the energy momentum conservation from the diffeomorphism invariance of the action, however I don't understand a ...
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### Gauge symmetries not from promotion of global symmetries

The most intuitive example of a gauge symmetry is such where you take a theory that has some global symmetry, and ask what needs to be done for this symmetry to be local. This procedure involves the ...
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### Do Lorentz rotations transform the Gamma matrices $\gamma_a$?

Do local Lorentz rotations (see below definition) actually transform the Dirac Gamma matrices? If so, how can they collude with coordinate transformations to make the Gamma matrices $\gamma_a$ ...
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### If gravity is a gauge theory, what is the Lie group? [duplicate]

Here I asked a question. In one curious comment, I see a statement that gravity is a gauge theory. However, my definition (based on what I read till date) of a gauge theory is a field theory which is ...
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### Gauge dependence of the Einstein tensor and the Riemann/Ricci curvature tensors in non-linear general relativity

The Einstein field equations are given by (with assuming $\Lambda = 0$), $$R_{ab} - \frac{1}{2} R g_{ab} = \kappa T_{ab}.$$ The principle of general covariance states that the form of these ...
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### Why are the Klein-Gordon equations warranted from the conservation of the energy-momentum tensor?

If we have an action with a scalar field non-minimally coupled to the gravity: $$\int dx^4 \sqrt{-g}(-\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}\zeta R\phi^2-V(\phi)).....(1)$$ varying ...
209 views

### Special relativity and diffeomorphism invariance

In studying general relativity (GR) we learn that the Einstein-Hilbert (EH) action $S_{EH}=\int_{M}\mathrm{d}v_{g}R$ (where $\mathrm{d}v_{g}=\mathrm{d}^{4}x\sqrt{-g}$, with $g$ the metric tensor) is ...
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### Diffeomorphism invariance of scattering amplitude in bosonic string theory

It is mentioned in Polchinski's book (vol 1) that the diffeomorphism invariance of the scattering amplitude (see Polchinski, vol 1, eq 5.3.9) follows from the equation of motion of $b_{ab}$ (see ...
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### In general relativity, are two pseudo-Riemannian manifolds physically equivalent if they are isometric, or just diffeomorphic?

In Carroll's Appendix B, he says You will often hear it proclaimed that GR is a "diffeomorphism invariant" theory. What this means is that, if the universe is represented by a manifold $M$ with ...
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### Is is true Superstring theory does not satisify diffeomorphism invariance?

So it is well known that string theory contains General Relativity in the classical limit. And assuming the spin-2 fields all couple correctly to the other fields this means it is diffeomorphism ...
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### Why the volume of a region is not a diffeomorphism invariant? (LQG)

In loop quantum gravity, the volume operator for a given region is not a diffeomorphism invariant. But classically we know that volume is a scalar quantity under a diffeomorphism even if we take the ...
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### How can you show diffeomorphism invariance of closed string field theory?

String Field theory if it predicts General Relativity should have 26D space-time diffeomorphism invariance (presumably). How can one show that Closed String Field Theory has this symmetry? (Besides ...
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### Question on how to think about diffeomorphism invariance

I know that GR must be diffeomorphism invariant, which (in my own words) means that GR, and by extension any observable, should not care about what coordinate system one chooses to use. Suppose I ...
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### Is general relativity resulted from diffeomorphism invariance?

Any action expressed as the integral of a 4-form in 4-dimensional spacetime is diffeomorphism invariant. For example the following 4-form topological (Pontryagin) action $$S = \int F\wedge F$$ is ...
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### Diffeomorphism invariance & solutions to EFEs

I’ve read (in Sean Carroll’s GR notes, and several other places), that general relativity (GR) is diffeomorphism invariant. By this, it is meant that, if $\phi:M\rightarrow M$ is a diffeomorphism, ...
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### Diffeomorphism & Weyl transformations in the 2D worldsheet of string theory and the existence of conformal gauge

D. Tong's notes on string theory, chapter 5 (PDF), feature the following in introducing the symmetries used in the Faddeev-Popov method: We have two gauge symmetries: diffeomorphisms and Weyl ...
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### Is there any example of a physical theory which isn't invariant under translations?

Isn't it trivial that all physical theories in spacetime are invariant under local translations? Is there an example of a theory which isn't invariant under translations? Please, take note that I'm ...
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### What is a diffeomorphism invariant action made from a single vector field?

Given an single vector field $A_\mu(x)$ is it possible to make a diffeomorphism invariant action in 4 dimensions? In the same way that General Relativity is diffeomorphism invariant? My first guess ...