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16
votes
1answer
224 views
Why is there no theta-angle (topological term) for the weak interactions?
Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken?
8
votes
3answers
48 views
Does the complex 3-sphere have a complex structure modulus?
This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical ...
2
votes
1answer
129 views
The topology of a “closed” universe - is it really closed?
The spatial part of the positive curvature FRW metric has the form
\begin{equation}
ds^2=\frac{dr^2}{1-(r/R)^2}+r^2d\Omega^2
\end{equation}
or
\begin{equation}
ds^2=R^2(d\chi^2+\sin{\chi}^2d\Omega^2)
...
5
votes
0answers
33 views
What is the importance of studying degeneration on $M_g$
Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$.
It seems to be important in physics to study ...
9
votes
5answers
196 views
Where do theta functions and canonical Green functions appear in physics
In the beginning of Section 5 in his article, Wentworth mentions a result of Bost and proves it using the spin-1 bosonization formula. This result provides a link between theta functions, canonical ...
11
votes
1answer
45 views
Relationship between Weak Cosmic Censorship and Topological Censorship
The weak cosmic censorship states that any singularity cannot be in the causual past of null infinity (reference).
The topological censorship hypothesis states that in a globally hyperbolic, ...
11
votes
2answers
334 views
The entropic cost of tying knots in polymers
Imagine I take a polymer like polyethylene, of length $L$ with some number of Kuhn lengths $N$, and I tie into into a trefoil knot. What is the difference in entropy between this knotted polymer and ...
8
votes
2answers
393 views
Is spacetime simply connected?
As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn.
This falls into the ...
0
votes
1answer
167 views
A question on smooth 1-manifolds
Consider two people living on two different smooth 1-manifolds $S$ and $T$ as shown in figure 1. The manifold $S$ is a bump function joining the points $A$ and $B$ and the manifold $T$ is formed by ...
8
votes
3answers
807 views
Can spacetime be non-orientable?
This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
6
votes
4answers
913 views
Shape of the universe?
What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...
29
votes
6answers
1k views
What is known about the topological structure of spacetime?
General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions:
What topological restrictions do Einstein's equations ...
13
votes
7answers
2k views
Applications of Algebraic Topology to physics
I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most ...
