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Topological Theta Term as a Topological Quantum Field Theory?

It is well known that the theta term $\int d^4x\frac{\theta}{4\pi}Tr[F\wedge F]=\int d^4x\frac{\theta}{4\pi}\epsilon_{\mu\nu\sigma\lambda}Tr[F^{\mu\nu}F^{\sigma\lambda}]$ is a topological term, ...
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What implications might our existing in a simulated universe have on our universe's topology? [closed]

Have there been any coherent speculations on what the universe containing the simulation might be like, and how our own universe might be described within it? This being without the naive assumptions ...
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2answers
68 views

Allowable spacetime deformations [closed]

What deformations are possible with spacetime? By 'deformation' I am referring to the kind of change in spacetime caused by the presence of a mass which deforms spacetime sufficiently to deflect ...
4
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0answers
56 views

Feynman Path integrals in space with holes in it [closed]

Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path ...
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0answers
19 views

Can one make a synthetic dimension “curl around” into a cylinder?

A really cool recent proposal, Synthetic Gauge Fields in Synthetic Dimensions. A. Celi et al. Phys. Rev. Lett. 112, 043001 (2014), arXiv:1307.8349, shows how you can simulate a synthetic ...
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1answer
88 views

Question about universe expansion

In general relativity, we cannot determine the global structure of the universe (since it is not flat), therefore all measurements and observations are only meaningful locally. In particular, we can ...
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2answers
348 views

The Aharonov-Bohm effect is purely classical, right?

Every discussion I've ever seen of the Aharonov-Bohm effect makes a big deal of its being a quantum effect with no classical analogue. But as far as I can tell it is present already at the classical ...
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0answers
35 views

$\mathbb{Z}_2$ topological insulators which obey inversion symmetry as well

According to Fu & Kane (2006), systems with simultaneous time-reversal invariance and inversion symmetry have their $\mathbb{Z}_2$ topological invariant given by the product of the parity ...
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287 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
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17 views

2D CFT for nontrivial topology

What is a systematic way to calculate a general $N$-points correlation function of 2D CFT for a nontrivial topology? Piece by piece of this can be found in many different CFT and String Theory ...
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1answer
39 views

Is the $2\pi$ disclination topologically stable for a 2d nematic liquid crystal?

For a three dimensional liquid crystal, a $2\pi$ or charge $1$ disclination is topologically unstable. The is generally explained as the disclination can lose its core singularity by "escaping from ...
5
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1answer
201 views

“Topological” notions in physics

I've been trying to make sense recently of the usage of 'topological' in various fields of physics, and get sort of an intuition for what this means in context. This all boils down to my main question ...
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2answers
66 views

Is an achronal set contained in its own causal future?

I use Wald's notation: $I^+$ is the chronological future and $J^+$ is the causal future. My confusion arises from the following passage in Wald (1984): Now, let $S$ be a closed, achronal set ...
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1answer
157 views

Why doesn't topological phase transition break any symmetry? Hidden symmetry?

This question may be superficial. However why all people saying this without a proof? Just like the "hidden variables" assumption in quantum mechanics, can one disproof that there is no hidden ...
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2answers
128 views

What is the connection between geometry of physical space and Hilbert space?

In Quantum Mechanis (QM), the dynamical variables are the (quantized) coordinates $x_j$ and their canonical conjugate $p_j = -i\partial_j$ with the commutation relation $[x_j,p_k]=i\delta_{jk}$ ...
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2answers
177 views

Is a spinor in some sense connected to space?

Spinors transform under the representation of $SL(2,\mathbb{C})$ which is the double cover of the Lorentz group $SO(1,3)$ - or in the non-relativistic case under $SU(2)$, the double cover of $SO(3)$. ...
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4answers
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Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
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1answer
44 views

Is a black hole really a hole in space? [closed]

What if when a supernova occurs, instead of it condensing into a singularity it creates enough force to tear a hole into the fabric of space? Is a black hole just what is sounds like, a hole in space? ...
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0answers
36 views

Validity of topological thermodynamics?

I've been reading some material by R. Kiehn, developing a topological approach to non-equilibrium thermodynamics through Cartan forms, where the fundamental claim is that irreversible processes are ...
7
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1answer
704 views

geometry inside the event horizon

I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a schwarszchild black hole. I would appreciate any insights or corrections to the above. ...
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1answer
300 views

Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
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4answers
1k 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 ...
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0answers
62 views

Quantum phase space

Classical phase space is defined as a space in which all possible states are represented. Every state corresponds to a unique point in the phase space. On the other hand, in quantum mechanics every ...
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0answers
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What is the latest findings on the topology and size of the universe?

The paper G. Aslanyan & A.V. Manohar, The Topology and Size of the Universe from the Cosmic Microwave Background, JCAP 06 (2012) 003, arXiv:1104.0015, uses the 7-year WMAP data. Has any ...
3
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1answer
159 views

Topologically distinct Feynman diagrams

Are these two diagrams topologically distinct? I consider $\phi^4$ theory and use the minimal subtraction renormalization scheme. A vertex corresponding to counterterm $-\imath \frac{m^2 ...
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0answers
39 views

Euclidean AdS space in Poincaré coordinates

I have read anti-de Sitter (AdS) space and its Euclidean version both in Global and Poincaré coordinates. For Lorentzian case it is clear how one Poincaré patch cover only one half of the whole AdS ...
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0answers
41 views

Topology of a bit

From a math perspective, it seems obvious that the electric field (or voltage which ever) of a bit in a computer, when its in a stable 0, or 1 state, must have a singularity, a set of points where the ...
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0answers
76 views

Manifold for Schwarzschild and Bertotti-Robinson

In short: what is the manifold in discussion for Schwarzschild metric $$ ds^2 = -(1-\frac {2M}r)dt^2 + \frac1{1-\frac{2M}r} dr^2 + r^2 (d\theta^2 + \sin^2 \theta d\phi^2)$$ and Bertotti-Robinson ...
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2answers
392 views

Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
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0answers
67 views

Is the metric-induced topology relevant at all in a (psuedo) Riemannian manifold? [duplicate]

A (pseudo) Riemannian manifold is a tuple: $$(M,g)$$ where $M$ is a smooth manifold (in particular, a topological space with an atlas) and $g$ is a (pseudo) Riemannian metric tensor. It is apparent ...
3
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0answers
38 views

How to work with singular gauge transformations in QFT [closed]

I was recently considering a problem analogous to the Aharonov-Bohm (AB) effect but in the context of quantum field theory. Consider then Dirac electrons minimally coupled to an AB flux and described ...
2
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1answer
89 views

The relationship between the structure of spacetime and the existence of spinor field?

We all know that the existence of spinor fields implies that spacetime must be time-orientable. Thus that spacetime is time-orientable is a necessary condition for existence of spinor fields. Geroch, ...
3
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1answer
76 views

What are the definition and examples of topological excitation?

I read topological excitation in wiki, while it's too brief. What is the precise definition of topological excitation? And can give me some examples and explain why they are topological excitation? ...
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1answer
228 views

Why isn't the path integral defined for non homotopic paths?

Context In the Aharonov Bohm effect, there is a solenoid which creates a magnetic field. Since the electron cannot be inside the solenoid, the configuration space is not simply connected. Question ...
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39 views

Is there an analytical expression for the conductivity of the surface of topological insulators?

I have a question about the conductivity on the surface of Topological Insulators (TI): Is it accurate to model the conductivity by the Drude model (I read a paper that modeled the conductivity with ...
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3answers
3k views

What is the shape of a black hole?

I was thinking; what shape does a black hole have?. By 'Shape', I mean its form (e.g, circle , cylinder, sphere, torus, etc..). We usually think of black holes as if they're plugholes (e.g, a flat ...
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2answers
167 views

Proof of quantization of magnetic charge of monopoles using homotopy groups

Suppose we place a monopole at the origin $\{{\bf 0}\}$, and the gauge field is well-definded in region $\mathbb R^3-\{0\}$ which is homomorphic to a sphere $S^2$. Then the total manifold is $U(1)$ ...
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0answers
66 views

Topological implications of symbolic represenation of the relativity

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal ...
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74 views

How to calculate topological charge?

For a complex vector field in two dimensions with one or more phase singularity - a point where the field amplitude is zero and the phase is undefined - how do you explicitly calculate the total ...
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1answer
137 views

Betti multiplets in Kaluza Klein compactifications

It is well known that if the compactification manifold of a supergravity theory has non-zero Betti numbers, this may lead to the so called Betti multiplets in the spectrum of the low dimensional ...
4
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2answers
191 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
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4answers
246 views

Liouville's theorem and preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? By Liouville's theorem, the total phase space volume is ...
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2answers
338 views

Topology of phase space

Context: From Liouville's integrability theorem we know that: If a system with $n$ degrees of freedom exhibits at least $n$ globally defined integrals of motion (i.e. first integrals), where all ...
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0answers
304 views

A Theorem Due to Hodge: Hawking/Ellis

This is probably quite an obscure question but hopefully somebody has a simple answer. I'm studying the proof of the topology theorem on black holes due to Hawking and Ellis (Proposition 9.3.2, p. 335 ...
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2answers
1k views

Book covering Topology required for physics and applications

I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
3
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1answer
80 views

Permutations of two identical particles in two dimensions

In three spatial dimensions there are only two possible statistics: Bose-Einstein and Fermi-Dirac. This is the fact related with the statement that first homotopic group of 3-dimensional configuration ...
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0answers
38 views

Bound states and extensive field configurations

What are extensive field configurations in QFT (instantons, monopoles etc.)? What is the difference in description of their contribution in path integral value or in $n$-point operator functions ...
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1answer
58 views

What's the definition of incompleteness of a coordinate system and a spacetime?

I always see in GR textbooks that some coordinates or some spacetime is incomplete, such as Rindler spacetime and spacetially flat FRW universe with only positive cosmological constant. This ...
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6answers
3k 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 ...
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4answers
3k views

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.