Questions tagged [scale-invariance]

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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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{...
• 505
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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. ...
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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 ...
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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 $$\phi_n(xb^{-1}) = b^{\Delta_n}\phi_x(x)$$ ...
96 views

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/...
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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 ...
• 11.8k
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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 ...
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1 vote
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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?
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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})...
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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 ...
1 vote
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 ...
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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 ...