Linked Questions
3
votes
0
answers
871
views
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 ...
- 12.9k
1
vote
0
answers
472
views
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 ...
- 12.3k
18
votes
5
answers
2k
views
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 ...
- 49.4k
16
votes
5
answers
3k
views
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 ...
- 521
13
votes
1
answer
2k
views
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 ...
- 1,539
22
votes
1
answer
4k
views
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.
...
- 6,071
5
votes
2
answers
1k
views
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?
- 1,892
4
votes
4
answers
2k
views
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
votes
1
answer
3k
views
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 ...
- 49.4k
10
votes
1
answer
1k
views
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}...
- 1,081
4
votes
1
answer
2k
views
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 $(M,g)$ ...
- 1,764
3
votes
2
answers
1k
views
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 ...
- 4,780
5
votes
1
answer
2k
views
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 $\...
- 3,093
2
votes
1
answer
818
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 ...
- 3,093
3
votes
2
answers
602
views
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 ...
- 519