All Questions
Tagged with mathematical-physics differential-geometry
211
questions
0
votes
0
answers
35
views
Index theorem of Callias operator in physics
In the article "On the index type of Callias-type operator" (https://doi.org/10.1007/BF01896237) Anghel study the index of a Callias type operator over an odd dimensional complete ...
- 31
0
votes
0
answers
64
views
Looking for video courses on general relativity, aimed at a mathematician crowd [closed]
I am a mathematician, working in symplectic geometry.
I am looking for online avalible video recordings of courses in general relativity, which are geared towards an audience of mathematicians.
...
1
vote
0
answers
122
views
On which bundle do QFT fields live?
In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
- 61
2
votes
2
answers
158
views
Non-orientability in electromagnetism
I'm currently studying E&M and I have a question related to the mathematical formalism of the theory. Electrodynamics depends heavily on the divergence and Stokes's theorem which in their ...
- 37
2
votes
1
answer
164
views
(Time-)Orientability in the Language of Fiber Bundles
I'm currently studying spin geometry through Hamilton's book Mathematical Gauge Theory. At a given point, Hamilton considers a pseudo-Riemannian manifold, which I'll take to be Lorentzian in $d=3+1$ ...
- 22.1k
2
votes
0
answers
135
views
Einstein's gravity Lagrangian invariance under the change of differential structure
I came across an article claiming the appearance of singularities in the energy-momentum tensor $T_{\mu \nu}$ as a result of changing the differential structure:
I wonder what symmetry or current (in ...
- 1,268
1
vote
1
answer
96
views
Conformal Transformation of Torsion
It is well known that under a conformal transformation, we have
$$\tilde{g}_{\mu \nu}=\Omega^2 g_{\mu \nu}, \; ; \tilde{w}_{\mu}=w_{\mu}-\frac{1}{\alpha} \partial_{\mu} \log(\Omega^2),$$
where $\...
- 689
3
votes
1
answer
143
views
Is the Godel universe Wick rotatable?
Take Wick Rotatability being as the way defined in the article by Helleland:
Wick rotations and real GIT
Is the Gödel universe Wick rotatable according to this definition?
- 1,268
7
votes
2
answers
164
views
Equivalent definition of Hawking quasi-local mass
I actually asked the following question at MathSE but didn't receive any response. My question is really about why the definition (2) below can be derived from the definition (1). Specifically, I don'...
- 159
4
votes
1
answer
273
views
Physical motivation for the definition of Spin structure
I'm pretty confused about the motivations behind defining a spin structure on a manifold. Let me explain.
In quantum mechanics, particles are represented by irreducible unitary projective ...
- 123
1
vote
1
answer
196
views
Why the Double Covering?
It is known mathematically that given a bilinear form $Q$ with signature $(p,q)$ then the group $Spin(p,q)$ is the double cover of the group $SO(p,q)$ associated to $Q$, and that $Pin(p,q)$ is the ...
- 1,611
3
votes
1
answer
804
views
Pre-requisites for V.I. Arnold's mathematical methods for classical mechanics
I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, ...
3
votes
0
answers
188
views
HaMiDeW coefficients - recursive calculation of the coincidence limits
In his book Aspects of Quantum Field Theory in Curved Spacetime Stephen Fulling calculates the coincidence limit $[a_1]$ and gives an idea of how $[a_n]$ with $2 ≤ n$ can be found recursively.
Since ...
8
votes
1
answer
429
views
Gauge Theory determined by Gauge Group and Representation: What about specifying the bundle?
I have the following question. In physics, when one talks about (Yang-Mills) gauge theories, one often states that it is enough to specify the following data:
The gauge group $G$, which is usually a ...
- 854
1
vote
2
answers
216
views
Doubt on the geometry of "quantum phase space"
In Jose & Saletan's "Classical Dynamics", they show the global structure of Hamiltonian mechanics: you then have a $Q$ manifold (configuration space), and the phase space structure is ...
- 3,085