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19 views

Transformation law for the eigenfunction representation of dilations (scale transformations) in CFT

On page 32 section 2.1.2. of http://arxiv.org/abs/hep-th/9905111 a representation $\phi(x)$ for the conformal group is chosen such that $D\phi(x) = -i \Delta\phi(x) $. After that it is stated that ...
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19 views

Implication of breakdown of scale invariance for problems with intrinsic length or time scales?

According to Wikipedia article on scale invarince, the equations for electric (and magnetic) fields : $$\nabla^2\vec{E}=\frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial ...
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1answer
21 views

CFT conformal weight vs. scaling dimension

I was wondering if anybody could clarify what the difference between the conformal scaling dimension $\Delta$ and the conformal weight $h$ is? Is it correctly understood that $\Delta$ is related to ...
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0answers
27 views

Scale invariance and stress energy tensor

I have seen in a paper [1] that in a quantum field theory scale invariance takes place provided the stress energy tensor is traceless. How this is true? References: "INFINITE CONFORMAL SYMMETRY IN ...
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0answers
38 views

Scale invariance

Physically why should scale invariance break down at the Planck limit? If not what are the other possibilities to save the quantum granularity of spacetime? I would really appreciate professional ...
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0answers
37 views

The scale anomaly and dependence on scale

The scale anomaly states that if we have renormalizable theory without dimensionful function, which is scale invariant, then corresponding quantum theory may lost this symmetry because of ...
0
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1answer
103 views

Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
3
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1answer
74 views

Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
3
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1answer
98 views

Is $\phi^4$ theory in 4d conformally invariant at the classial level?

I used to believe the three following statements to be true (at the classical level only): From scale invariance full conformal invariance follows. Scale invariance is present if there are no ...
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1answer
420 views

Is scale invariance an axiom in physics?

Is scale invariance axiomatic within physics, and if so, how does it get around the transition from the microscopic, quantum world, to the macroscopic, classical world?
3
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0answers
31 views

Scale-covariant decomposition of capacitance

I'm wondering if there is any good insight of how to evaluate a given capacitive geometry in such a way that it would be expressed as a function that depends only on two components: as a geometric ...
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2answers
79 views

Scale relativity vs scale invariance

What is the difference between Nottale's "scale relativity", and the ordinary concept of scale invariance e.g. that appears in conformal field theory?
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1answer
510 views

Is John Nash's “Interesting Equation” really interesting?

As recently mentioned in the news, before his passing, John Nash worked on general relativity. According to the linked article John Nash's work is available online from his webpage. His work is ...
2
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1answer
101 views

Does scale invariance imply massless or continuous mass distribution?

$\newcommand{\ket}[1]{\lvert #1 \rangle}\newcommand{\bra}[1]{\langle #1 \rvert}\newcommand{\scp}[2]{\langle #1 \vert #2 \rangle}$ In his 2008 slides (PDF), Tzu-Chiang Yuan mentions the following on p. ...
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0answers
151 views

Chiral Scale and Conformal Invariance in 2D QFT

I am reading a paper by Hofman and Strominger. In the appendix A, I have reproduced the equations (A10). Now they made a statement that "The Jacobi identity can be used to show that $O_h$ and $O_p$ ...
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1answer
274 views

Scale invariance in QFT?

About scale invariance in "beyond the standard model". At the base of the analysis is the principle of scale invariance. So what is being said: what if there were another sector of the theory that ...
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1answer
115 views

Universality classes

I would like to ask about the universality classes. I know that these are the statistical models which describes different phase transitions with different critical exponents. But I would like to know ...
0
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1answer
92 views

Ising model scale invariance

Could someone help me and explain what is the connection between divergence of the correlation length, and the scale invariance. So why will in the critical point the system show scale invariance if ...
2
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2answers
139 views

Simplifying effect of a hidden Weyl symmetry in a QFT on curved spacetime

We consider AdS$_{d+1}$ in Poincaré coordinates: $$ ds^2=\frac{1}{z^2}\left(-dt^2+dz^2+dx_{d-1}^2\right), $$ where we set the AdS radius to unity. We study a scalar in this background with action $$ ...
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0answers
69 views

Are the following terms, related to scale invariance and renormalization in QFT, equivalent?

Which of the following terms are equivalent? and in what cases/limits do the non-equivalent terms become equivalent? A) a scale invariant quantum field theory. B) a conformal quantum field theory. ...
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0answers
65 views

Noether current scale transform of EM

I'm trying to solve a question about scale tranform of free EM. I got the next trnaform rules (these two line where EDITed later) $\delta x = -bx$ $\delta A = bA$ the current I got $D^\mu = ...
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1answer
179 views

How is the electric potential of a localized charge distribution scaled when scaling the geometry of the problem?

I am trying to find the potential at a point on the surface of a charged polygon (rectangular). I have find a solution to the problem, but it relies on the following statement: If the potential at ...
1
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1answer
258 views

Why does Weyl invariance imply a traceless energy-momentum tensor?

I've begun to self-study String Theory from Polchinski and Becker, Becker and Schwarz. I don't see why the fact that the Polyakov action is invariant under Weyl transformations is related to the ...
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1answer
243 views

From which dimensionful constants does proton mass arise?

It is well known that the most of the proton (or any other hadron with light quarks) mass is not made up from quark masses, but it is dynamically generated by QCD mess inside. I've also heard that, ...
2
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1answer
336 views

Dilaton field and Scale symmetry breaking

I have read at some places that a dilaton field is associated with the spontaneous breaking of scale symmetry in a theory. (While others would be difficult to trace right now, the most easily ...
2
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0answers
44 views

Coupling constraint in massless Thirring Model in (1+1) Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (Link to the PRD paper http://prd.aps.org/abstract/PRD/v11/i8/p2088_1), he pointed out that the massless Thirring Model ...
3
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1answer
128 views

Massless Thirring Model in 1+1 Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, ...
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1answer
177 views

What is Scale invariance? [closed]

Could anybody tell me what does scale invariance means? Is there any book or article that describes [ and gives examples ] about it.
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0answers
106 views

RG flow from a UV scale invariant field theory to a gapped phase in the IR

On the section 3 of http://arxiv.org/abs/1309.2921 the authors consider the RG flow from a scale invariant field theory in the UV to a gapped theory in the IR. The theory is couple to a background ...
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1answer
447 views

Scale invariance plus unitarity implies conformal invariance?

What has the reaction been towards the recent paper claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?
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0answers
209 views

Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is ...
17
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1answer
2k views

What is the difference between scale invariance and self-similarity?

I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
3
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0answers
189 views

Questions about classical and quantum scale invariance

This is kind of a continuation of this and this previous questions. Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
0
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0answers
83 views

Scale invariance Vs Conformal invariance [duplicate]

Possible Duplicate: Why does dilation invariance often imply proper conformal invariance? What exactly is the difference between the two? Can someone give an example of a theory which is ...
17
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3answers
1k views

Why does dilation invariance often imply proper conformal invariance?

Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
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5answers
953 views

Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...