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1

Below that regime, we have the strongly coupled regime where perturbative approaches fail, due to the large value of coupling constant $\alpha_S$. The same is related to the QCD $\beta$ function via this relation. The behavior as a function of the energy scale looks roughly like this. Any perturbation expansion in this regime would give a divergent series, ...


3

This formula follows the usual heuristic discretization rules (here written in 1D): $$\tag{1} \text{discrete var.}\qquad i\in\{1, \ldots,N\}, ~~x_i=i\Delta ~~\longrightarrow~~x~\in~[0,L] \qquad \text{cont. var.},$$ $$\tag{2} \text{sum}\qquad \sum_{i=1}^N ~~\longrightarrow~~ \int_0^L \! \frac{dx}{\Delta} \qquad\text{integral},$$ $$\tag{3} ...


0

The RG is not a group, it's a semi group so you can only go in one direction, the one that actually renormalize. Here you can use the relation K'(K) for your flow. but if you use K(K'), you will have something wrong because the RG procedure that give this relation as no physical meaning. it's as if you add spin in your Ising chain. When you do RG, ,you ...


0

The only mass scales are the mass of the electron $m_e$, and, if we consider other kind of interactions of a fermion (here the electron) with a massive gauge vector boson (ex : $Z$ for the weak interaction), or a massive scalar ( scalar electrodynamics), you would have this boson mass $m_B$ too. However, the chiral symmetry being exact for $m_e=0$, we ...


1

As far as I have understood the topic, the fact that the correction to the mass is going with the log is not the point. The point is that it is proportional to the mass of the electron itself (The log enters in this argument via the fact that it doesn't blow up as fast as e.g. quadratic divergence). You will know that the chiral symmetry is exact for $m=0$, ...


5

The QFT for the scalar is considered to be massive for a very good reason: it is infinitely unlikely for the mass to vanish. There is no symmetry principle that would protect the scalar field from acquiring a generic mass. (The gauge symmetry is the principle that protects the masslessness of the photon but the scalar fields can't sacrifice to lose ...


4

The key thing is that you need to be working with canonically normalized fields in order to use the power counting arguments. Let's expand GR around flat space \begin{equation} g_{\mu\nu} = \eta_{\mu\nu} + \tilde{h}_{\mu\nu} \end{equation} The reason for the tilde will become clear in a second. So long as $\tilde{h}$ is "small" (or more precisely so long ...


4

The relativistic Schr\:odinger equation is known as the Klein-Gordon, and is the pre-quantized version of the quantum field theory of a noninteracting scalar field. If you attempt to couple this to general relativity, you get what is known as the Einstein-Klein Gordon equation. If you attempt to na\:ively quantize this theory, you encounter all of the ...



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