All Questions
11
questions
0
votes
0
answers
83
views
Gauge transformation and Kaluza-Klein metric
The Kaluza-Klein metric, by reduction, can be written as a $(4+m) \times (4+m)$ symmetric matrix, where $m$ is the dimension of the additional spacetime (if we decompose $M_D = M_4 \times M_m$). It ...
- 980
5
votes
1
answer
317
views
Lagrangian for Gauge theory of gravity
There are a number of questions here discussing gravity as a gauge theory of the Lorentz group. I am trying to find the Lagrangian this gauge produces, and the other discussions stop just short of ...
- 1,538
2
votes
0
answers
78
views
Michio Kaku: Global Symmetry on Yang-Mills theory and gravity theory uniqueness (?)
In p.6 of Michio Kaku book Introduction to Superstrings and M-Theory-Springer (1998), he said
Yang-Mills theory and gravity theory are the unique solution to two simple geometric statements:
Global ...
- 4,336
6
votes
1
answer
321
views
Why Einstein action is not Yang-Mills action for gauge theory of Poincaré algebra?
It is well known, how to construct Einstein gravity as gauge theory of Poincare algebra. See for example General relativity as a gauge theory of the Poincaré algebra.
There are
Construction of ...
- 5,707
4
votes
1
answer
358
views
Why aren't gravitons spin 1?
Expressing the metric as $g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$, assuming $h_{\mu \nu} \ll 1$ we can write the Einstein Hilbert action to leading order in $h_{\mu \nu}$ and quantize the ...
- 11.6k
20
votes
3
answers
3k
views
Yang-Mills vs Einstein-Hilbert Action
The classical Yang-Mills action is of the form
$$S=\frac{1}{2g^2}\int_{\mathcal{M}}\text{tr}\left[F\wedge\star F\right]\\
=\frac{1}{4g^2}\int\mathrm{d}^dx\sqrt{g}\,\text{tr}\left[F^{\mu\nu}F_{\mu\nu}\...
- 8,490
7
votes
2
answers
528
views
Is there a notion of torsion for Yang-Mills/gauge connection?
In theories of gravity, the Riemannian/metric connection, is allowed to have torsion, of which the Levi-Civita connection is the particular torsion-free case.
In the gauge theoretic description of ...
- 174
0
votes
1
answer
2k
views
Gauge transformations in gravity [duplicate]
The Maxwell equations are invariant under the transformation
$$A_{\mu} \rightarrow A_{\mu} - \dfrac{1}{e}\partial_{\mu}\alpha(x)$$
where $\alpha(x)$ is a phase transformation varying from point to ...
- 5,257
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
37
votes
4
answers
14k
views
Gravity as a gauge theory
Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory).
Why should "classical" gravity be some (non-trivial or "special" or extended)...
- 6,581
6
votes
3
answers
585
views
Could general relativity and gauge theories in principle be covered in one course?
It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the ...
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