All Questions
12
questions
0
votes
0
answers
38
views
Bitensors at three or more space-time points
Bitensors, i.e. tensors at two points that have indices belonging to either of them, have been used in the literature quite a bit and there are many calculations involving them. They are the go-to ...
4
votes
1
answer
152
views
Is quantization chart-dependent?
I have a bit of confusion because when doing QFT and QFT in curved spaces this particular issue seems to be avoided.
I have this feeling that when we quantize a theory, we somehow choose a chart and ...
6
votes
1
answer
558
views
QFT on curved spacetime, uniqueness of spacelike hypersurface
Consider the Lagrangian of a real, scalar field coupled to gravity via the metric $g_{\mu\nu}$ and covariant derivative $\nabla_\mu$
$$\mathcal{L} = \sqrt{-g} (-\frac{1}{2} g^{\mu\nu} \nabla_\mu \phi \...
- 136
1
vote
0
answers
70
views
Can quantum effects lead to modification of gravity?
Consider a modified theory of gravity with the action $$S = \int d^4x \sqrt{g}~R^{\alpha}$$ where $\alpha > 1$. Now, the vacuum equations of motion is same as the usual GR. So, the perihelion of ...
- 1,200
0
votes
1
answer
269
views
Spinors and Tensors: what is the form of spin transformation matrix?
The (covariant) vector transformation law is given by:
$$V^{'}_{\mu} = t^{\nu}\hspace{0.1mm}_{\mu'}V_{\nu} =\frac{\partial x^{\nu}}{\partial x'^{\mu}}V_{\nu} \tag{1}$$
where the transformation is ...
- 3,085
0
votes
0
answers
55
views
What is the relation of differential geometry to General Relativity and Quantum Field Theory? [duplicate]
We know that Yang Mills Theory forms the basis of the Standard Model of Physics, which describe the interaction of elementary particles at high energies, of course not including gravity. Yang Mills ...
5
votes
1
answer
223
views
Hamiltonian covariant time translation
I am working on vector fields in curved manifolds and arrive at the following question:
Why is it that we demand the Hamiltonian to generate time translations:
$$[i\mathcal{H}, A_\mu] = \partial_t ...
- 1,323
14
votes
2
answers
958
views
Differential geometry of Lie groups
In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they ...
- 141
2
votes
1
answer
106
views
Compatibility conditions of spinors and Riemannian Metrics
I came across an interesting article by Montesinos (J. Geom. Phys. 2 (1985), no. 2, 145–153.). In it, he finds that spin structures (as lifts of $SO(4)$) are not compatible with all Riemannian metrics ...
- 5,389
4
votes
0
answers
371
views
Dirac equation in curved space-time with Torsion
I am looking for pedagogical references in which Dirac equation in space-time with curvature and torsion were discussed.
17
votes
2
answers
7k
views
Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This $-i\bar{\gamma}^{\mu}\Gamma_{\...
user21119
8
votes
3
answers
1k
views
Extending General Relativity with Kahler Manifolds?
Standard general relativity is based on Riemannian manifolds.
However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
- 17.7k