All Questions
39
questions
1
vote
1
answer
72
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 ...
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
$$D_{\mu}V^{\nu}=\partial_{...
- 101
2
votes
0
answers
41
views
Coframe fields and spin connection as gauge fields and gauge invariance of torsion 2-form
I have questions about differential geometry calculations. If there is any misunderstanding of mine in the contents below, please let me know and help me to fix it.
Let's consider a 3-dimensional ...
- 33
1
vote
0
answers
61
views
Reparametrization invariance of Einbein action [closed]
I'm going through David Tong's online lecture notes on String theory. At the end of section 1.1.2, where he introduces the einbein action
$$S=\frac{1}{2} \int d\tau (e^{-1}\dot{X}^2-em^2),\tag{1.8}$$
...
- 11
1
vote
1
answer
159
views
Reasoning about spin coupling on curved space
In the course of QFT i learnt that the gauge field emerges from the need of a gauge invariance in the action, as we use the covariant derivative in minimal coupling. Now i'm studying how spin fields ...
- 165
2
votes
1
answer
186
views
Gauge-fixing condition invariant under auxiliary gauge transformation
In quantum gravity one usually splits the metric $g= \bar{g}+h$ into a background field $\bar{g}$ and a fluctuation field $h$. In order to obtain a propagator one has to gauge fix the action (e.g. ...
- 494
0
votes
1
answer
121
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Einstein field equations from covariant derivative of a general linear gauge transformation
A general linear transformation is given by
\begin{align}
\psi'(x) \to g \psi(x) g^{-1},
\end{align}
The gauge-covariant derivative associated with this transformation is
\begin{align}
D_\mu \psi=\...
- 1,538
7
votes
4
answers
1k
views
Question on connections in general relativity and particle physics
$1$ Introduction
It seems that when you learn General Relativity all the technology of bundles are irrelevant (at least in elementary discussions as $[1]$, $[2]$, $[3]$ and others). But, even the ...
- 3,085
1
vote
0
answers
104
views
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 ...
- 3,085
5
votes
0
answers
146
views
Complex, Holomorphic connection, and Symplectic — a not-so-Kähler manifold?
While studying mathematical physics, I wondered whether if there is a mathematical theory for a manifold that
has a complex structure [almost complex structure $J^\mu{}_\nu$ with vanishing Nijenhuis ...
- 564
1
vote
0
answers
105
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Is the Poincaré gauge theory a real gauge theory in the mathematical sense?
When studying Poincaré gauge theory using Milutin Blagojevich's book on "Gravitation and gauge symmetries" we find an interesting line of thought. But to get that I need to set some ...
- 113
6
votes
7
answers
901
views
What are the analogues of $F_{\mu\nu}$ in General Relativity?
In electromagnetism, the measurable gauge-invariant quantities are the electric and magnetic fields or the six independent components of the field strength tensor $F_{\mu\nu}$. What are the analogues ...
- 11.8k
0
votes
0
answers
246
views
Derivation of the transformation rules for vielbein and spin connection
I have been taking a course on General Relativity. Recently, I was given the following homework assignment, which reads
Derive the following transformation rules for vielbein and spin connection:
$$\...
- 159
4
votes
3
answers
370
views
Local Lorentz invariance of General Relativity
Consider the gravitational action as an integral over a differential 4-form $$ S = \int_{\mathcal{M}} \star F_{ab}\wedge e^a \wedge e^b$$ where $\star F_{ab} = \epsilon_{abcd} F^{cd}$ and $F$ is the ...
- 1,190
1
vote
1
answer
202
views
Gauge-fixing conditions in Einstein-Cartan gravity
What are the gauge-fixing conditions one needs to impose on the tetrad one-form $e^a$ and the spin-connection one-form $\omega^{ab}$ while working in the Einstein-Cartan formalism where both are ...
- 1,190