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2
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1answer
72 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 Unparticle Phenomenology (PDF), Tzu-Chiang Yuan ...
3
votes
0answers
128 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 $O_p$ ...
0
votes
1answer
92 views

Scale invariance in QFT?

I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the ...
0
votes
1answer
53 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
votes
1answer
53 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 ...
1
vote
2answers
116 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 $$ ...
3
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0answers
52 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. ...
1
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0answers
55 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 = ...
0
votes
1answer
46 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 ...
3
votes
1answer
100 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
votes
1answer
174 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
votes
0answers
41 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
votes
1answer
101 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, ...
1
vote
1answer
131 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.
5
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0answers
89 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 ...
10
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1answer
351 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?
1
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0answers
165 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
votes
1answer
1k 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
votes
0answers
168 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
76 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 ...