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Cyclic Universe Problems

In Penroses's hypothesis, at the end of each iteration the universe undergoes a conformal transformation, meaning distances are rescaled. If I am right, it implies that a planet from the previous ...
Nayeem1's user avatar
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Could a universe be expanding if its physics were scale invariant?

Imagine a universe where every field is massless and has scale-invariance. Would the expansion/contraction of the universe still be happening there? would it be detectable? Would it affect the ...
P. C. Spaniel's user avatar
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What is the definition of a conformal symmetry? [duplicate]

I have been very confused by this after some recent reading. So as far as I know, a conformal transformation (according to the definition in di Francesco et. al.'s book on CFT) is an active coordinate ...
QFTheorist's user avatar
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Reference request scale anomaly

Can anyone recommend some books, notes and review-oriented papers on scale anomaly, with a view towards its relation to renormalization? Such as an anomaly perspective on RG, Callan-Symanzik equations ...
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Field transformation under conformal transformation

In 1 (see references below), I'm trying to derive how a spinless field transforms under a conformal transformation, specifically eq. (2.41). CFT references/lectures are the most confusing I've seen ...
mathemania's user avatar
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Confusion regarding scale symmetry for certain charge configurations

I had a question on symmetry operations that exactly resembles this post. The selected answer there mentions the required symmetry operation to be scale symmetry, and says: An infinite plate looks ...
archthegreat's user avatar
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1 answer
91 views

State-Operator Correspondence and symmetry in CFT in general dimension

Let us assume to have a QFT ($\mathcal{L}$) with translational, Lorentz, scale and conformal invariance. I ask because we can, for example the free scalar free theory, canonically quantize the system ...
ssm's user avatar
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How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?

In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold: $$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
Генивалдо's user avatar
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Scale transformation of scalars in curved backgrounds

I am puzzled by the concept of scalar fields that arise in conformal field theory in curved backgrounds. In general relativity, so far as I understand it, a scalar field is basically a function ...
Kuroush Allameh's user avatar
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What is the difference between scale invariance and scale free?

A question several years ago asked, "What is the difference between scale invariance and self-similarity. It appears that a new term has become popular in recent years, which is "scale ...
Chris 's user avatar
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5 answers
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Does pure Yang-Mills have a scale?

Consider pure Yang-Mills (YM) in 4 dimensions. The YM mass gap problem (as described in https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf) tells us that this is supposed to have a mass-...
dennis's user avatar
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Scale transformation of the scalar field and gauge field

I am reading this paper: "Magnetic monopoles in gauge field theories", by Goddard and Olive. I don't understand some scale transformations that appear in Page 1427. Start from the energy ...
Daren's user avatar
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Inflation in new aeons (cyclic cosmology)

I have a question pertaining to Penrose's ideas about cyclic cosmology. As predicted therein, the end of each cycle comes about when massive particles are extinct and time is no longer measured. What ...
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A sense in which inverse square law forces are scale invariant?

For a fixed separation, the gravitational acceleration between two uniform spheres of density $\rho$ is proportional to their radius $r$. But since angular sizes and distances across the celestial ...
user1247's user avatar
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4 votes
1 answer
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Ising model rescaling

Consider the 2D classical Ising model. It's understood that there is a critical temperature $T_c$, and that the correlation length $\xi(T)$ defined by: $$\langle \sigma_i \sigma_j \rangle_\mathrm{...
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1 answer
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Conserved current of quartic interaction QFT ($φ⁴$-Theory)

The Lagrangian of the real massless $φ⁴$-theory is \begin{align} L=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\lambda\phi^4 \end{align} Therefore the action integral has the global symmetry \begin{...
Aralian's user avatar
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1 answer
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Do conserved currents have to be primary?

In many texts about CFT it is proven that spin-1 conserved currents have the dimension $d-1$. In the proof it is used that, sometimes only implicitly, the current $J^\mu$ is a primary operator. ...
Bronsteinx's user avatar
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Metric in dilatation transformation of massless scalar field

The lagrangian density of the massless real scalar field is \begin{align} L = \frac{1}{2}\eta^{\mu\nu}\partial_\mu\Phi\partial_\nu\Phi = \frac{1}{2}\partial_\mu\Phi\partial^\mu\Phi. \end{align} I want ...
Aralian's user avatar
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Conformal invariance and tracelessness of the energy-momentum tensor: contradictory statements

Before starting my question, let me define a couple terms to avoid the confusion that usually accompanies this topic: I define the $c$-number valued energy-momentum tensor as $T^{\mu\nu} = \frac{2}{\...
nodumbquestions's user avatar
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Momentum as ladder operator in CFT

I'm following these lectures: https://arxiv.org/abs/1601.05000. In eq, 3.19 the author writes $$ [D,\mathcal{O}(0)] =-i\Delta \mathcal{O}(0),\tag{3.19} $$ where $D$ is the generator of dilations and $\...
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1 answer
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Intuitive interpretation of the scaling dimension of an operator?

I am reading Field Theories of Condensed Matter Physics by Fradkin and in equation (4.10) it shows that an operator transforms irreducibly under scalings as $$\phi_n(xb^{-1}) = b^{\Delta_n}\phi_x(x)$$ ...
physics_fan_123's user avatar
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What does the non-commuting nature of the translation and dilation generators mean for the scaling dimension of a field?

I am reading about CFTs from the book by Di Francesco, Mathieu and Senechal and in page 98 was introduced to the conformal group and the algebra of the generators. In particular, we have the dilation/...
newtothis's user avatar
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2 answers
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Does the stress energy tensor scale with the metric tensor?

Question I had some thoughts from a previous question of mine. If I have a metric $g^{\mu \nu}$ $$g^{\mu \nu} \to \lambda g^{\mu \nu}$$ Then does it automatically follow for the stress energy tensor $...
More Anonymous's user avatar
10 votes
2 answers
763 views

Why are CFTs not usually studied in momentum space?

Conformal symmetry in QFT has been extremely useful for physics. However, while most of QFT is usually done in momentum space, CFTs are usually studied in position space or in terms of Mellin ...
Ari's user avatar
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How to show that in 2D CFT the marginal operator must have $(h,\bar h)=(1,1)$?

A related post might be What are marginal fields in CFT? where Qmechanic♦ pointed to Ginsparg secion 8.6. However, I heard about two argument. Claim 1:In a $D$ dimension CFT, the marginal operator ...
ShoutOutAndCalculate's user avatar
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0 answers
109 views

Space-Time Symmetries and Scaling

Typically, when a course examines symmetries of space-time and their consequences (e.g. symmetries of Lagrangians and conserved quantities), either the Lorentz group or the Poincaré group are ...
Uroc327's user avatar
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0 answers
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What is the physical significance of conformal invariance of conformally invariant field theories?

Edited Question The absence of certain terms can make a field theory conformally invariant. For example, the absence of a mass term in the Maxwell action makes it conformally invariant. Here is a nice ...
Solidification's user avatar
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1 answer
231 views

Scale invariance in curved spacetime?

Question What does it mean for the metric to be scale invariant in curved spacetime (in the sense when I say a property is scale invariant in thermodynamics)? I'm confused as to how to define this. It ...
More Anonymous's user avatar
4 votes
1 answer
308 views

What does the pole in the running of the QED coupling represent?

In the case of QCD, the $\Lambda_{QCD}$ introduces a scale in the theory that can be also modified in presence of strongly interacting fermions. This mass-scale breaks the classical scale invariance ...
Bastam Tajik's user avatar
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Local scale invariance without conformal anomaly

I need to know if conformal symmetry can be localized in the same manner that global symmetries like $SU(2)$ is localized and gauge bosons pop up?(I assume the trace anomaly doesn't violate the scale ...
Bastam Tajik's user avatar
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2 votes
1 answer
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Is nonlocality consistent with scale invariance?

For sure I'm excluding gravity at first step, the question is that if nonlocality is compatible with scale invariance. At the classical and quantum levels for field theory in Minkowski spacetime. Then ...
Bastam Tajik's user avatar
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2 votes
1 answer
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Intuition for the trace-free energy-momentum tensor condition in CFTs

It is a textbook exercise to show that \begin{equation}T^{\mu}_{\,\,\,\mu}=0 \end{equation} is a sufficient condition for there to be a conserved current associated with a dilation symmetry. This ...
Luke's user avatar
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1 answer
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What is the meaning of power laws in physics?

I know the basic meaning of a power law. Scale invariance. Also that with negative exponents, bigger events occur more rarely, like in say earthquakes. But I can't seem to find more physical ...
BitterDecoction's user avatar
1 vote
0 answers
63 views

How to check the conformal prefactor in a correlation function?

In CFT it is usual practice to extract the so-called conformal prefactor from the correlators in order to isolate a function which depends only on the cross-ratios. For example the $4$-point function ...
Pxx's user avatar
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4 votes
1 answer
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Intuition behind power-law scale invariance

I have seen this notion of a scale-invariant power law curve exhibiting the property that $f(cx) = a(cx)^{-k} = c^{-k}f(x)$, and I am confused about how I should be thinking of this as "scale-...
physics_fan_123's user avatar
0 votes
1 answer
123 views

How to amend General Relativity to include a position-dependent gravitational 'constant' $G$?

What is the best way to amend General Relativity to include a variable gravitational 'constant' $G$, that depends on the positions of all other masses? That is, if the amount of 'bending of space-time'...
John Hunter's user avatar
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2 votes
2 answers
120 views

Representation of dilations

I am having some trouble getting some signs right on the representation of the dilation operator on a field. Let us follow the conventions of Joshua D. Qualls https://arxiv.org/abs/1511.04074. ...
Ivan Burbano's user avatar
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1 vote
1 answer
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Scale invariance beyond the critical point

Using Anderson localization as an example, I understand how scale invariance comes into play at a critical point - at a critical point, the localization length $\xi$ (the average "radius" of ...
BGreen's user avatar
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3 votes
2 answers
1k views

Proving the energy-momentum tensor for a conformal field theory is traceless

A trick to derive Noether currents that is frequently used in conformal field theory literature is the following: suppose we have an action $S[\phi]$ which has the infinitesimal symmetry $\phi(x) \...
Hermitian_hermit's user avatar
2 votes
0 answers
35 views

Boundary condition for $\Box\vec{E}(t,\vec{x})=0$ that preserves scale-invariance

In short, this is a question about the symmetry of a differential equation preserved by its boundary condition. In free space, the vector wave equation satisfied by the electric and the magnetic field ...
Solidification's user avatar
7 votes
2 answers
1k views

What does scale invariance or non-invariance of electromagnetism physically imply?

According to Wikipedia, classical electromagnetism is scale-invariant. I understand what it means mathematically as explained in Wikipedia. But what does it really imply physically? Next, here it ...
Solidification's user avatar
1 vote
1 answer
73 views

What dictates the efficiency of a semiconductor?

Semiconductors can be used for a heat exchange but are less efficient than a Freon air-conditioning system. What dictates this efficiency?
user avatar
2 votes
1 answer
1k views

Proof that free scalar field is conformally invariant

So, under conformal transformations $$x\mapsto x'\\ \phi\mapsto\phi'(x')=\Omega^{(2-D)/2}\phi(x),$$ where $$\eta_{\mu\nu}\frac{\partial x^\mu}{\partial x^{'\alpha}}\frac{\partial x^\nu}{\partial x^{'\...
Ivan Burbano's user avatar
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0 answers
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Are infinitesimal dilatation transformations local?

In quantum field theories, a local transformation of a scalar field $\phi(x)$ is a transformation that involves the field and its derivatives at same point. See for instance Weinberg's QFT textbok, ...
Adam's user avatar
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1 vote
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Is there a valid solution to Einstein's equations for this cosmological model?

The cosmological model below has been developed in order to explain the flatness problem. At first it's from Newtonian considerations, then a solution of the Friedman equations is looked for $$\left(\...
John Hunter's user avatar
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1 vote
1 answer
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Another static solution of the Friedmann equations - interpretation of $p=-\rho c^2$

Looking for solutions of the Friedmann equations $$(\frac{\dot a}{a})^2+\frac{kc^2}{a^2} = \frac{8 \pi G \rho+\Lambda c^2}{3}, \tag{1}$$ $$\frac{\ddot a}{a} = \frac{-4 \pi G}{3} (\rho + \frac{3p}{c^2})...
John Hunter's user avatar
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4 votes
3 answers
846 views

What determines the magnitude of the atmospheric scale height of a planet?

What determines the magnitude of the atmospheric scale height of a planet? https://en.wikipedia.org/wiki/Scale_height says that: "Approximate atmospheric scale heights for selected Solar System ...
Matthew Christopher Bartsh's user avatar
1 vote
0 answers
96 views

Experimental Test for the cyclic $G_{earth}$ prediction of a Cosmological Model

Can anyone suggest a way to measure or rule out a tiny cyclic variation in the earth’s gravitational constant $G_{earth}$, predicted by an alternative cosmological model? It’s an annual cyclic ...
John Hunter's user avatar
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17 votes
5 answers
4k views

Does a slowed down version of small stone falling in water look the same as a big rock falling in real time?

I was wondering: If you let a small stone drop on a body of water, record it on film, and replay the scene in slow motion, will it be possible to see the difference with a huge rock that falls, in ...
Deschele Schilder's user avatar
1 vote
0 answers
92 views

Monte Carlo approach to determining mean free path of Lévy dust

Problem statement I am trying to determine the mean free path $\lambda$ of a so-called Lévy dust, i.e. $M$ points in a square $L\times L$ environment with distances between subsequent points ...
Johannes Nauta's user avatar