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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
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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 ...
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1answer
68 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, ...
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1answer
130 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 ...
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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 ...
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1answer
100 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
118 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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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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323 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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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 ...
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1answer
931 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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151 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 ...
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70 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 ...
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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 ...