All Questions
Tagged with gauge-theory general-relativity
157
questions
3
votes
1
answer
72
views
Can Black Holes with electroweak or strong interactions exists in General Relativity or in Supergravity?
During my Master's degree, we studied Black Holes as solutions of Einstein-Maxwell equations, and I was wondering if it would be possible to also add strong or electroweak forces in the classic non-...
- 770
1
vote
1
answer
71
views
Geometrical interpretation of gauge fields of spin other than 2
Gravitation can be interpreted as a gauge theory with a spin 2 graviton field. This graviton field in general relativity is also interpreter as a Riemannian metric. Do other gauge theories also have ...
1
vote
1
answer
70
views
Gravitational waves from metric perturbation
I have just been introduced to gravitational waves from metric perturbations and I have some questions about gauge symmetry and solutions in a given gauge.
Consider a metric on the form $g_{\mu\nu} = \...
- 69
0
votes
2
answers
122
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Renormalizability of Quantum Gravity
At the end of chapter 6 on p. 210 in David's Griffiths' book Introduction to Elementary Particle Physics he says that 't Hooft proved that all gauge theories are renormalizable. I have also read ...
- 39
0
votes
1
answer
64
views
What is the relation between gauge field and Levi-Civita connection?
In field theory, covariant derivative is something like
$$D_{\mu}\phi=(\partial_{\mu}-igA_{\mu})\phi$$
while in differential geometry, covariant derivative is something like
$$D_{\mu}V^{\nu}=\partial_{...
- 101
0
votes
0
answers
83
views
Gauge transformation and Kaluza-Klein metric
The Kaluza-Klein metric, by reduction, can be written as a $(4+m) \times (4+m)$ symmetric matrix, where $m$ is the dimension of the additional spacetime (if we decompose $M_D = M_4 \times M_m$). It ...
- 980
14
votes
3
answers
2k
views
How do physicists mathematically define gravitational waves?
When one first encounters gravitational waves in a standard GR lecture or a standard textbook like Carroll's "Spacetime and Geometry", they are often "defined" as follows: The ...
- 357
2
votes
0
answers
41
views
Coframe fields and spin connection as gauge fields and gauge invariance of torsion 2-form
I have questions about differential geometry calculations. If there is any misunderstanding of mine in the contents below, please let me know and help me to fix it.
Let's consider a 3-dimensional ...
- 33
1
vote
0
answers
61
views
Reparametrization invariance of Einbein action [closed]
I'm going through David Tong's online lecture notes on String theory. At the end of section 1.1.2, where he introduces the einbein action
$$S=\frac{1}{2} \int d\tau (e^{-1}\dot{X}^2-em^2),\tag{1.8}$$
...
- 11
15
votes
1
answer
345
views
What is the full algebra of BRST-invariant observables for general relativity?
The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to ...
- 126k
4
votes
0
answers
211
views
Justifying the transverse-traceless gauge
For weak gravitational fields, we can assume the metric is some perturbation of flat space: $g_{ab} = \eta_{ab} + h_{ab}$. Following Schutz's argument, you can incorporate a small coordinate ...
- 151
1
vote
0
answers
81
views
Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
- 858
4
votes
1
answer
299
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Standard model and gravity gauge theory
I will briefly explain my understanding on the subject.
In the following explanation i refer to the Poincarè group meaning the group:
$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin^+(1,3)$$
The ...
- 1,611
2
votes
1
answer
151
views
Is there a general argument for why non-dynamical degrees of freedom show up in the propagation of massless gauge bosons?
In both spin-1 and spin-2 gauge theories, the gauge bosons (e.g. the photon & gluon and the graviton respectively) have two physical degrees of freedom, which can be observed quantum mechanically ...
- 858
2
votes
0
answers
89
views
Noether's second theorem: its extension [closed]
From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry groups. A classic, even historical, example is the invariance group of Riemannian spacetimes, i.e. the set ...
- 81