Questions tagged [research-level]

The research-level tag applies to questions that arise in graduate and post-secondary work. These questions often require domain-specific knowledge and could not be answered from a general source or may be beyond the level typically covered by Wikipedia and other popular sources. Research-level questions should not require new or groundbreaking research and results to answer.

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163
votes
5answers
19k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
123
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0answers
6k views

Linear sigma models and integrable systems

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow, I faced difficulties in penetrating the literature... I'd highly appreciate any help ...
114
votes
1answer
7k views

Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
107
votes
0answers
5k views

Experimental test of the non-statisticality theorem?

Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
83
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12answers
13k views

What is spontaneous symmetry breaking in quantum systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
81
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0answers
3k views

Orbits of maximally entangled mixed states

It is well known (Please, see for example Geometry of quantum states by Bengtsson and Życzkowski ) that the set of $N$-dimensional density matrices is stratified by the adjoint action of $U(N)$, where ...
65
votes
1answer
3k views

On the Coulomb branch of ${\cal N}=2$ supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D ${\cal N}=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs ...
56
votes
1answer
1k views

What is the upper-limit on intrinsic heating due to dark matter?

Cold dark matter is thought to fill our galactic neighborhood with a density $\rho$ of about 0.3 GeV/cm${}^3$ and with a velocity $v$ of roughly 200 to 300 km/s. (The velocity dispersion is much ...
55
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0answers
1k views

Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
51
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5answers
17k views

What does it mean for a Hamiltonian or system to be gapped or gapless?

I've read some papers recently that talk about gapped Hamiltonians or gapless systems, but what does it mean? Edit: Is an XX spin chain in a magnetic field gapped? Why or why not?
50
votes
2answers
1k views

Analog Hawking radiation

I am confused by most discussions of analog Hawking radiation in fluids (see, for example, the recent experimental result of Weinfurtner et al. Phys. Rev. Lett. 106, 021302 (2011), arXiv:1008.1911)...
44
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6answers
3k views

What are some critiques of Jaynes' approach to statistical mechanics?

Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? I was wondering about good critiques of Jaynes' approach to statistical ...
43
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8answers
6k views

Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
42
votes
1answer
3k 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?
42
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5answers
2k views

What is the use of a Universal-NOT gate?

The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
41
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5answers
12k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in the condensed matter physics community. I'm familiar with the imaginary time, coherent state, and path integral ...
40
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5answers
11k views

A pedestrian explanation of conformal blocks

I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
36
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6answers
3k views

Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?

Is there a theorem that says that QFT reduces to QM in a suitable limit? Of course, it should be, as QFT is relativisitc quantum mechanics. But, is there a more manifest one? such as Ehrenfest's ...
36
votes
1answer
4k views

State of Matrix Product States

What is a good summary of the results about the correspondence between matrix product states (MPS) or projected entangled pair states (PEPS) and the ground states of local Hamiltonians? Specifically, ...
36
votes
2answers
4k views

Large and small gauge transformations?

I've a questions about the difference between small and large gauge transformations (a small gauge transformation tends to the identity at spatial infinity, whereas the large transformations don't). ...
35
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6answers
4k views

Could gravity be an emergent property of nature?

Sorry if this question is naive. It is just a curiosity that I have. Are there theoretical or experimental reasons why gravity should not be an emergent property of nature? Assume a standard model ...
35
votes
2answers
929 views

experimental bounds on spacetime torsion

Did Gravity Probe B provide any bounds on Einstein-Cartan torsion? is a non-zero torsion value at odds with the results regarding frame-dragging and geodetic effects?
34
votes
4answers
447 views

Models of neutrinos consistent with OPERA's results

I guess by now most people have heard about the new paper (arXiv:1109.4897) by the OPERA collaboration which claims to have observed superluminal neutrinos with 6$\sigma$ significance. Obviously this ...
34
votes
3answers
1k views

Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
32
votes
3answers
2k views

Continuum theory from lattice theory

I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
32
votes
7answers
1k views

An entropy of the Wigner function

Is there an entropy that one can use for the Wigner quasi-probability distribution? (In the sense of a phase-space probability distribution, not - just von Neumann entropy.) One cannot simply use $\...
32
votes
1answer
3k views

Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero ...
31
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1answer
2k views

Sympletic structure of General Relativity

Inspired by physics.SE: Does the dimensionality of phase space go up as the universe expands? It made me wonder about symplectic structures in GR, specifically, is there something like a Louiville ...
31
votes
5answers
3k views

Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
30
votes
5answers
5k views

Wormholes & Time Machines - for *experts* in GR/maths

EDIT: Further clarification in the context of answers/comments received to 20 Jan has been appended EDIT: 21 Jan - Response to the Lubos Expansion appended [in progress, not yet complete] EDIT: 23 ...
30
votes
2answers
3k views

Is there a T-dual of Witten's twistor topological string theory?

In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four ...
28
votes
2answers
7k views

Topological Charge. What is it Physically?

I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
28
votes
1answer
6k views

How Fundamental is Spin-Orbit Coupling to Topological Insulators?

I'm well aware this is a very active area of research so the best answer one can give to this question may be incomplete. Topological states in condensed matter are well-known, even if not always ...
27
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0answers
448 views

Minimal strings and topological strings

In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
26
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5answers
5k views

Simple models that exhibit topological phase transitions

There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
26
votes
1answer
3k views

Diff(M) as a gauge group and local observables in theories with gravity

In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical ...
26
votes
1answer
2k views

Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
26
votes
1answer
827 views

Sigma Models on Riemann Surfaces

I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action \begin{align*}...
25
votes
1answer
980 views

Mermin-Wagner theorem in the presence of hard-core interactions

It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...
25
votes
1answer
3k views

Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?

Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in ...
24
votes
2answers
2k views

Do topological superconductors exhibit symmetry-enriched topological order?

Gapped Hamiltonians with a ground-state having long-range entanglement (LRE), are said to have topological order (TO), while if the ground state is short-range entangled (SRE) they are in the trivial ...
24
votes
1answer
1k views

Asymptoticity of Pertubative Expansion of QFT

It seems to be lore that the perturbative expansion of quantum field theories is generally asymptotic. I have seen two arguments. i)There is the Dyson instability argument as in QED, that is showing ...
24
votes
1answer
830 views

Vasiliev Higher Spin Theory and Supersymmetry

Recently there is renewed interest in the ideas of Vasiliev, Fradkin and others on generalizing gravity theories on deSitter or Anti-deSitter spaces to include higher spin fields (utilizing known ...
24
votes
1answer
443 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each $x\in\...
23
votes
5answers
748 views

Connections and applications of SLE in physics

In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
23
votes
3answers
732 views

Geometric Langlands as a partially defined topological field theory

I have heard from several physicists that the Kapustin-Witten topological twist of $N=4$ 4-dimensional Yang-Mills theory ("the Geometric Langlands twist") is not expected to give rise to fully defined ...
23
votes
2answers
316 views

Significance of the hyperfinite $III_1$ factor for axiomatic quantum field theory

Using a form of the Haag-Kastler axioms for quantum field theory (see AQFT on the nLab for more details), it is possible in quite general contexts to prove that all local algebras are isomorphic to ...
23
votes
4answers
2k views

Which exact solutions of the classical Yang-Mills equations are known?

I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups. It would be nice if someone can find a review article discussing all such solutions EDIT: I ...
23
votes
2answers
2k views

Can one force the electric quadrupole moments of a neutral charge distribution to vanish using a suitable translation?

For a system of electric charges $q_i$, at positions $\mathbf{r}_i$, with a nonzero net charge $Q=\sum_i q_i$, one can define a "centre of charge" in the obvious way as $$ \mathbf{r}_c=\frac{1}{Q}\...
23
votes
0answers
340 views

Super Lie-infinity algebra of closed superstring field theory?

Bosonic closed string field theory is famously governed by a Lie n-algebra for $n = \infty$ whose $k$-ary bracket is given by the genus-0 (k+1)-point function in the BRST complex of the string. One ...

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