Recently, Prof. David Tong has released a set of lecture notes on particle physics. In the introduction, it has been claimed that notes cover things in high school mathematics, and it is true. However, a little more than high school, but a keen learner would find it suitable to learn through the process.
You may check the notes and bookmark it if you are interested;
The major paper, on which I was working, is finally out yesterday night. It is on unparticle physics. Just because that I am now quite attracted by this scheme of unparticle physics, which I have described here.
You can read and enjoy the paper following this;
We use Feynman diagrams to calculate some scattering or interaction, as we show in Fig 1. We try to maximize our knowledge of interaction by doing some integrals and eventually getting the matrix elements, which then is used for calculating the cross-sections ($\sigma$) and many more things.
We have now touched the RG [4]. There is a lot more motivation for RG, including practical application in high-energy physics and condensed matter.
Footnotes;
[1] These are called self-interactions. We try to minimize these self-interactions. However, studying these loops gives us more intuition of particular theory when needed.
[2] Both Quantum Field Theory and Statistical Field Theory.
[3] This quest was why quarks could not be found in open space in free form, while leptons are found in their free form.
[4] This post was just a visualization of a brief history and crux of renormalization. There are many counter-intuitive feelings in a person who is studying RG. There is much more to discuss and much more to doubt.
Feel free to comment about questions and typos.
It is fascinating to read about abstruse Unparticle Physics. But it is very uncommon for an ordinary person to even hear the name "Unparticle Physics". It was first coined and explained by Howard Georgi in 2007 in a short paper. However, it is not a self-contained subject, it involves interesting, challenging, intricate topics like Scale Invariance and Banks-Zaks Field.
A scale-invariant theory is scale conserving theory. If you know the Mandelbrot set, you know they are scale-invariant. But a more simple example would be a circle and a radius. You can zoom in to the circle and still get the same angle ($\theta$).
That is pretty much the idea of scale invariance. It comes with another invariance called Conformal Invariance. Conformal Invariance preserves the angle in a transformation ignoring the Lorentz transformations. Scale-Invariant theories are also pretty much Conformal Invariant theory. Any high energy theory contains at least two fields, in this scenario, Standard Model and Bank-Zaks Field. The latter field is called theory with non-trivial IR fixed point. Both the fields interact with the exchange of particle $M_{\mu}$, but under the energy $M_{\mu}$ they don't interact, they can, but couplings are suppressed.
Unparticle Physics has been structured on the $M_{\mu}$ scale. It was wise to use Bank-Zaks operators as Unparticle operators in an Effective Field Theory with below $\Lambda_{\mu}$ energy. The paper shows that it matches onto. For an $O_{BZ}$ operator with mass dimension we have $O_{\mu}$ with low dimensions.
The propagator for unparticle physics is also quite useful. And the important note is that unparticle stuff ignores the gauge interactions from Standard Model. There are many things one can note from Unparticle Physics. One of them is its "Weirdness". It assumes particles with scale invariance that we haven't seen yet. It is impossible, right now, to test this theory. However, if we ever achieve it, it is going to be tremendous. One can ask, whether particles with conformal invariance exists or such questions.
In another paper, Georgi showed a simple interaction $e^+ e^- \rightarrow \mu^+ \mu^-$. It showed different scales of cross-sections, considering different symmetries and propagators. I will recommend you to check that paper.
References
