All Questions
39
questions
23
votes
3
answers
2k
views
Why does the analogy between electromagnetism and general relativity differ if you consider them as gauge theories or fiber bundles?
Electromagnetism and general relativity can both be thought of as gauge theories, in which case there is a natural analogy between them:
(Strictly speaking, the gauge symmetry of diffeomorphism ...
- 48.4k
0
votes
1
answer
140
views
How large is the subset of flat spin connections?
In Poincare Gauge Theories spin connections take the role of the Levi-Civitta connection of GR for defining covariant derivatives. The GR can be formulated as a Poincare Gauge Theory which is called ...
- 3
7
votes
2
answers
532
views
Is there a notion of torsion for Yang-Mills/gauge connection?
In theories of gravity, the Riemannian/metric connection, is allowed to have torsion, of which the Levi-Civita connection is the particular torsion-free case.
In the gauge theoretic description of ...
- 174
8
votes
2
answers
1k
views
Einstein-Yang-Mills Connections
I am playing around with coupling a classical $SU(2)$ Yang-Mills theory to Einstein's equations.
Assuming spherical symmetry, the $SU(2)$ connection can be written
\begin{equation}
A = \omega(r)\...
- 1,609
7
votes
2
answers
260
views
Akin to gauge field, why GR's lagrangian is not $R_{abcd}R^{abcd}$? What's the mathematical or physical meaning of $R_{abcd}R^{abcd}$?
For gauge field theory, the Lagrangian of the gauge field is $$\mathcal{L}=-\frac{1}{4}\mathrm{tr}(\mathcal{F}_{\mu\nu}\mathcal{F}^{\mu\nu})=-\frac{1}{8}F_{a\ \mu\nu}F^{a \ \mu\nu}$$
The field ...
- 5,971
5
votes
0
answers
118
views
What is the status of gauged gravity [duplicate]
The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory.
We might be able to quantize gravity similarly. ...
- 1,487
12
votes
1
answer
3k
views
Infinitesimal transformations for a relativistic particle
The action of a free relativistic particles can be given by
$$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right),\tag{1.8}$$
with signature $(-,+,\ldots,+)$...
- 459
15
votes
1
answer
3k
views
Diffeomorphisms, Isometries And General Relativity
Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while.
Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
- 7,936
9
votes
2
answers
3k
views
What is the physical interpretation of harmonic coordinates?
When I see harmonic coordinates used somewhere, what should my association be?
Is there some general use or need to consider the harmonic coordinate condition?
I don't really see what's behind all ...
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