Linked Questions
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Does gravity have a gauge symmetry group? [duplicate]
In the Standard Model, U(1) corresponds to the electromagnetic, SU(2) to weak, and SU(3) to strong interactions. I realize that gravity is not a part of the Standard Model. However, sometimes gravity ...
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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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18
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5
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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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16
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5
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Lorentz Transformations Vs Coordinate Transformations
I'm really confused about Lorentz transformations at the moment. In most books on QFT, Special Relativity or Electrodynamics, people talk about Lorentz transformations as some kind of special ...
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13
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1
answer
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Geometric meaning of spin connection
A very short question: Does the spin connection that we encounter in General Relativity $$\omega_{\mu,ab}$$ have a geometric meaning? I am supposing it does because it comes from mathematical terms ...
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22
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1
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Why is it so coincident that Palatini variation of Einstein-Hilbert action will obtain an equation that connection is Levi-Civita connection?
There are two ways to do the variation of Einstein-Hilbert action.
First one is Einstein formalism which takes only metric independent. After variation of action, we get the Einstein field equation.
...
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5
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2
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1k
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Under what representation do the Christoffel symbols transform?
I often read the statement, that the Christoffel symbols aren't tensors. But then, under which representation do they transform?
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4
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4
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If gravitational waves are ripples in space-time, then electromagnetic waves are ripples in what?
If the answer is the electromagnetic field, then is it also ubiquitously present as space-time?
11
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In nonabelian gauge theory, does the ordinary or covariant derivative go into the statement of current conservation?
Before equation (77.35), Srednicki's QFT book says
We define the chiral gauge current $j^{a\mu}$ [where $a$ is a color index]. Its covariant divergence (which should be zero, according to Noether's ...
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10
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General relativity as a gauge theory of the Poincaré algebra
Let the Poincaré algebra be given without any factors of i as
$[P_\mu,P_\nu]=0$,
$[M_{\rho \sigma},P_\mu]=\eta_{\sigma\mu}P_\rho-\eta_{\rho\mu}P_\sigma$,
$[M_{\mu\nu},M_{\rho\sigma}]=\eta_{\nu\rho}...
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4
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1
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Is spacetime symmetry a gauge symmetry?
In previous questions of mine here and here it was established that Special Relativity, as a special case of General Relativity, can be considered as the theory of a (smooth) Lorentz manifold $(M,g)$ ...
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3
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2
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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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5
votes
1
answer
2k
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How to show that the Einstein-Hilbert action is diffeomorphism invariant?
It is often stated in texts on general relativity that the theory is diffeomorphism invariant (N.B., I am considering active diffeomorphisms), i.e. if the universe is represented by a manifold $\...
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2
votes
1
answer
818
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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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3
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2
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602
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What's the physical content in the invariance of spacetime interval in GR?
Spacetime interval in one co-ordinate system is given by : $$g_{\mu \nu} dx^{\mu} dx^{\nu} \tag{1}$$
$dx$ is some infinitesimal displacement vector between two events.
Spacetime interval after a ...
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4
votes
1
answer
544
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What is the Lie group of gravity?
If the lie group of the three gauge forces are $SU(3)×SU(2)×U (1)$, then what is the symmetry group of gravity? $SL(2,C)$?
Just a newbie in Lie groups.
2
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2
answers
652
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Laws of physics and diffeomorphism covariance
Up to my limited understanding, diffeomorphisms on a space-time manifold can be viewed as changes of coordinates. While studying general relativty, I read that the theory has diffemorphism covariance ...
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2
votes
1
answer
640
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What is the meaning of diffeomorphism invariance?
I have read a bunch of papers and I see "diffeomorphism invariance" and I cannot understand how it works.
For instance, in asymptotic safe quantum gravity, we make 2 assumptions:
...
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2
votes
2
answers
278
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If quantum gravity is a TQFT, why isn't the Wheeler-De Witt equation satisfied automatically?
It is often said that QG is a topological QFT: given a bordism between $D$-manifolds $\Sigma_1$ and $\Sigma_2$, QG assigns a unitary between the Hilbert spaces associated with $\Sigma_1$ and $\Sigma_2$...
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8
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387
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Definition of gravity path integral?
In a non-abelian gauge theory there is a "fundamental" gauge field $A_\mu^a$ with gauge index $a$ often called connection. Although $ A_\mu^a$ is not gauge invariant, gauge invariant quantities can be ...
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2
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1
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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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Doubt on the gauge group of Gravitation
(I wrote the introduction section for the sake of completeness, notation and study. The question per se, is written in the section "My Question")
Introduction
On the one hand of nature, we ...
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89
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Why is General Relativity considered a gauge theory? [duplicate]
Gauge theories are those which can be written with a Lie group as a symmetry group.
According to Sean M Caroll's book, I can find the Lorentz group or Poincare group. So can General Relativity be a ...
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0
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94
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Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
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0
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74
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Coordinate invariance in Physics
Let us consider a classical field theory on flat background spacetime. The action is
$$S[\Phi] = \int d^nx \mathcal{L}(\Phi,\partial_\mu\Phi).$$
Why shouldn't this action be independent of the chosen ...
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