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 ...

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3
votes
1answer
417 views

An odd relation with the epsilon/delta invariant tensors of SO(3)

The rotation group SO(3) can be viewed as the group that preserves our old friends the delta tensor $\delta^{ab}$ and $\epsilon^{abc}$ (the totally antisymmetric tensor). In equations, this says: ...
8
votes
1answer
740 views

Relativistic center of mass

Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case ...
4
votes
0answers
72 views

functional representations of free quantum fields

The free real quantum field, satisfying $[\hat\phi(x),\hat\phi(y)]=\mathrm{i}\!\Delta(x-y)$, $\hat\phi(x)^\dagger=\hat\phi(x)$, with the conventional vacuum state, which has a moment generating ...
11
votes
3answers
310 views

POVMs that do not require enlargement of the Hilbert space

The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
14
votes
1answer
992 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 ...
18
votes
2answers
198 views

Values of SM parameters at one certain scale

The general question is: What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
9
votes
1answer
168 views

How can one build a multi-scale physics model of fluid flow phenomena?

I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
8
votes
0answers
82 views

Pohlmeyer reduction of string theory for flat and AdS spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
6
votes
3answers
387 views

Modular invariance for higher genus

As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories: Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
6
votes
0answers
441 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
8
votes
2answers
167 views

Torsion and gauge invariant EM kinetic term

Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
8
votes
2answers
259 views

Wilson Loops in Chern-Simons theory with non-compact gauge groups

VEVs of Wilson loops in Chern-Simons theory with compact gauge groups give us colored Jones, HOMFLY and Kauffman polynomials. I have not seen the computation for Wilson loops in Chern-Simons theory ...
8
votes
1answer
533 views

Derivation of the basic equation for Witten diagrams

I could understand the derivation of the "bulk-to-boundary" propagators ($K$) for scalar fields in $AdS$ but the iterative definition of the "bulk-to-bulk" propagators is not clear to me. On is ...
6
votes
0answers
112 views

String landscape in different dimensions

For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to ...
6
votes
1answer
308 views

Uniqueness of the 5 string theories

This question combines several sub-questions, the common theme being: why the known 5 string theories are unique? Firstly, regarding heterotic theory. I understand the only allowed gauge groups are ...
47
votes
2answers
879 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), ...
7
votes
0answers
348 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
14
votes
1answer
687 views

Lagrangian for Euler Equations in general relativity

The stress energy tensor for relativistic dust $$ T_{\mu\nu} = \rho v_\mu v_\nu $$ follows from the action $$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu ...
11
votes
1answer
161 views

Some questions on a version of the O'Raifeartaigh model

This form is taken from a talk by Seiberg to which I was listening to, Take the Kahler potential ($K$) and the supersymmetric potential ($W$) as, $K = \vert X\vert ^2 + \vert \phi _1 \vert ^2 + ...
24
votes
4answers
1k 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 ...
16
votes
5answers
1k views

Applications of Geometric Topology to Theoretical Physics

Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold ...
6
votes
1answer
129 views

How does a geodesic equation on an n-manifold deal with singularities?

My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by: ...
10
votes
2answers
310 views

Nuclear physics from perturbative QFT

Is there a renormalizable QFT that can produce a reasonably accurate description of nuclear physics in perturbation theory? Obviously the Standard Model cannot since QCD is strongly coupled at nuclear ...
3
votes
1answer
102 views

Physics in high lepton chemical potential

I consider zero temperature and high lepton number chemical potential $\mu$. This results in a neutrino (or antineutrino, depending on the sign of the potential) "sea" filling a Fermi sphere in ...
6
votes
0answers
190 views

Is there precision experimental evidence for Furry's theorem — that only even degree VEVs are non-zero?

Is there precision experimental evidence for or contradicting Furry's theorem -- that only even degree VEVs are non-zero, specifically for the EM field?
7
votes
1answer
330 views

Where does the hidden supersymmetric sector of the MSSM come from?

At the end of Chapter 14 of the "Supersymmetry Demystified book" from Patrick Labelle it is mentioned that to constrain the number of allowed softly SUSY breaking terms, a shadow or hidden ...
7
votes
2answers
289 views

Simulation of QED

Can anyone point me to a paper dealing with simulation of QED or the Standard Model in general? I will particularly appreciate a review paper.
12
votes
1answer
556 views

What is a “free” non-Abelian Yang-Mill's theory?

I hope this question will not be closed down as something completely trivial! I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
10
votes
1answer
161 views

Quantum gravity at D = 3

Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization ...
8
votes
3answers
117 views

Depolarizing threshold for CSS codes

Many years ago, when CSS codes were first invented, the error threshold of p=0.11 was found when bit and phase flips are independent. Has a threshold yet been found for the case of depolarizing noise? ...
9
votes
1answer
283 views

AdS/CFT at D = 3

AdS/CFT at D = 3 (on the AdS side) seems to have some special issues which I bundled into a single question The CFT is 2D hence it has an infinite-dimensional group of symmetries (locally). The ...
9
votes
1answer
96 views

Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
7
votes
2answers
138 views

Group of symmetries of Lagrange's equations

Consider the following statements, for a classical system whose configuration space has dimension $d$: Lagrange equations admit a smaller group of "symmetries" (coordinate change under which ...
19
votes
1answer
415 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 ...
6
votes
1answer
322 views

Status of the little hierarchy problem

What is the current thinking on the little hierarchy problem in light of a potential Higgs mass above 120 GeV? A few years ago, at least, I remember various phenomenologists saying that this at least ...
5
votes
1answer
75 views

Interplay between the cosmological constant and “microscopic” properties of string vacua

As far as I understand, string phenomenology is usually concerned with compactifications of string theory, M-theory or F-theory in which the uncompactified dimensions form a 4-dimensional Minkowski ...
8
votes
1answer
94 views

Matrix geometry for F-strings

A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N ...
13
votes
1answer
104 views

Physical interpretation of superstrings

The scalar fields $X^\mu$ in bosonic string theory have a clear physical interpretation - they describe the embedding of the string in spacetime. Adding fermionic fields on the worldsheet is a ...
9
votes
4answers
1k views

The Schwinger model

The Schwinger model is the 2d QED with massless fermions. An important result about it (which I would like to understand) is that this is a gauge invariant theory which contains a free massive vector ...
11
votes
1answer
112 views

Higgs Field - Is its discovery truly “around the corner”?

Rather surprised I haven't seen many questions or discussion regarding the rumored confirmation of the Higgs field. As I understand it, the energies where they saw things were actually quite a bit ...
46
votes
0answers
2k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
5
votes
1answer
244 views

Convergence of quantum effective action to finite loop order

Consider the quantum effective action of a fixed QFT. If we compute it perturbatively to finite loop order $\ell$, we get a sum over an infinite number of Feynman diagrams. For example, the 1-loop ...
17
votes
6answers
1k views

Does Kaluza-Klein theory successfully unify GR and EM? Why can't it be extended to the Standard Model gauge group?

As a quick disclaimer, I thought this might be a better place to ask than Physics.SE. I already searched there with "kaluza" and "klein" keywords to find an answer, but without luck. As background, ...
4
votes
1answer
150 views

Derivatives of fluctuations about a condensate

Firstly I am not sure as to whether I am using the word "condensate" in the right context. In QFT contexts I think I see it getting used to mean the space-time independent solution which would solve ...
6
votes
1answer
561 views

Defining the ground state energy of a QFT

I would like to hear of some general discussion on how is the ground state and its energy defined in QFT and how does one go about finding it. (..at least in some simple cases I have seen the use of ...
12
votes
2answers
96 views

Numerical Analysis of Elliptic PDEs

I am looking for an elementary reference regarding issues of stability in numerical analysis of non-linear elliptic PDEs, particularly using the finite difference method (but something more ...
13
votes
0answers
107 views

Quantum statistics of branes

Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other What happens if we replace particles by ...
9
votes
1answer
127 views

Conformal QFTs for D > 2

Which conformal QFTs do we know for spacetime dimension d > 2? I know that for D = 4 we have N = 4 SYM and some N = 2 supersymmetric Yang-Mills + matter models. What is the complete list of such ...
4
votes
1answer
289 views

Massive excitations in Conformal Quantum Field Theory

Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of ...
6
votes
1answer
144 views

Optimality of the CHSH strategy

The maximum achievable probability of the Clauser-Horne-Shimony-Holt game is $\cos^2(\pi/8)\approx85.355\%,$ which can be proved with Tsirelson's inequality. But I don't imagine that this remained ...