Questions tagged [scaling]
Questions involving the laws which are scale invariant, i.e. that apply to different scales equally. Also laws that involve exponential behavior, expressed in terms of certain magnitudes to the power of certain exponents.
150 questions
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Why is the trace of the stress-energy tensor the generator of scale transformations?
I learn $d \geq 3$ conformal field theory on my own with some resources (like the big yellow book or Qualls' lectures). At one point, the authors talk about the stress-energy tensor and derive the ...
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${}$ What exactly is a dimension? [closed]
Intuitively, I understand that if something is measured in meters, it has the dimension of length, which we denote as $L$. For example, if we take length and time as fundamental dimensions, then ...
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How will the drag on an object flowing in air change if the object's volume is reduced to 1%? [closed]
How will the drag on an object flowing in air change if the object's volume is reduced to 1%?
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Justifying Zero Scaling Dimension for Fluctuation Fields
Suppose you have a theory where $\phi$ is just a fluctuation field. \begin{equation} S = \int d^dx dt (\partial_t \phi)^2 \end{equation} Using naive dimensional analysis we can set $[x] = 1$ and $[t] =...
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How does scaling a wire frame affect the frequency of a bead's periodic motion? [closed]
A bead is released from one end of a frictionless rigid wire frame fixed in a vertical plane, as shown in the diagram. The bead slides periodically due to gravity. The following details are given: The ...
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1answer
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4D Fourier transform for spectral decomposition
I can't make sense of this Fourier relation in 1+3 spacetime: $$\int_{F.C.}d^4 p\ e^{-i px} \rho(p^2)=\frac{1}{x^4}\ \ \to\ \ \rho(p^2)\propto p^2\ \ \ \ (1)$$ (where $F.C.$ stands for "forward ...
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Scaling transformation confusion [duplicate]
I'm reading the yellow book (CFT by Di Francesco) and I came across a bit of a confusing statement. Consider a scaling transformation $x^\mu \rightarrow x'^\mu = \lambda x^\mu$. Then the metric ...
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Four-point function in CFT, two constraints are missing
I am deriving the four-point functions, using translation and Lorentz invariance I start with the following form: $$ \langle \phi_1(x_1)\phi_2(x_2)\phi_3(x_3)\phi_4(x_4)\rangle=C_{1234}x_{12}^ax_{13}^...
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Regarding physical phenomena related to operators of the form $\exp(x\partial_x)$ [duplicate]
I am studying exponential operators, for example, of the form $\exp(x \partial_x)$. Do these operators appear or model any physical phenomena? or are they just abstract entities?
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Can students effectively model the temperature effects of passic cooling on a scale architectural model? [closed]
I am helping some students made models for a Science fair. They'll make 1:12 scale (one-scale) models of these in sculpey and wood: Roman court-houses with water features. A Persian wind catcher. ...
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Why do scalars scale?
The diffeomorphism invariance of scalars is often written as: $$ \phi'(x') = \phi(x).\tag{1}$$ However, while scaling transformation is a type of diffeomorphism, in many places (say Di Francesco, ...
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Scaled Hamiltonian and sped up evolution
Suppose there is a time-dependent Hamiltonian and the Schrodinger equation is solved. $$ i\hbar \partial_t U(t) = H(t) U(t) $$ Now, how easy is it to solve a scaled version of the Hamiltonian (e.g., $...
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How to prove that unit operators are the only operators with zero scaling dimension in an unitary CFT?
In David Simmons-Duffin's Phys 229 notes found on author's github here pg. 147 it is said that the free boson field $\phi$ in bosonic CFT has zero dimension but it is not the unit operator. So the ...
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Scaling equation for the external field H in an Ising like system [closed]
i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
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Using the RG equations to find the free energy scaling form of the 2D Ising Model
i am trying to calculate the scaling form of the free energy of the 2D Ising model, starting from it's RG equations: $$\frac{d u_I}{dl} = 2 u_I + u_t^2$$ $$\frac{d u_t}{dl} = u_t$$ $$\frac{d u_h}{dl} =...
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