All Questions
9
questions with no upvoted or accepted answers
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
3
votes
0
answers
318
views
GR as a gauge theory whose gauge group is $GL(4,ℝ)$ and whose gauge field are the Christoffel symbols $Γ_𝜇$ viewed as a $GL(4,ℝ)$-valued field
The answer to this question Is spacetime symmetry a gauge symmetry? makes the following claim:
One may indeed view general relativity as a gauge theory whose gauge group is $GL(4,ℝ)$ and whose gauge ...
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
2
votes
0
answers
54
views
Can the covariant derivative of General relativity be obtained from a $GL(4,\mathbb{R})$ transformation?
Is it possible to obtain general relativity as a gauge theory from the general linear group?
The starting point is:
$$
M'=GM
$$
where $M',M,G$ are elements of $GL(4,\mathbb{R})$.
I believe the second ...
- 1,548
1
vote
1
answer
73
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
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
1
vote
0
answers
106
views
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
1
vote
1
answer
803
views
Gauge dependence of the Einstein tensor and the Riemann/Ricci curvature tensors in non-linear general relativity
The Einstein field equations are given by (with assuming $\Lambda = 0$),
$$
R_{ab} - \frac{1}{2} R g_{ab} = \kappa T_{ab}.
$$
The principle of general covariance states that the form of these ...
- 11
0
votes
0
answers
248
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