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;
Curiosity is a priceless yet costly character that one can achieve by abolishing many senseless predefined characters. It is a fundamental gift that everyone should receive, and better to accept it now, not any old. In history, it is beautifully depicted how impeccable a person can be with his curiosity and ability to find what can't be found.
You, at some point, will or already have realized that being idle is also a curiosity. Not virtuous, yet you are finding, not consciously, the results for being nothing. That, however, never promotes you to do "nothing."
Curiosity drives more than it stops.
My cabinet couldn't afford fancy and expensive collections but was a pure collection of paintings, some books I considered worthy, some notebooks, and a book on 'F=ma.' I am sure the last piece in my anachronistic chronology was pure gold (Hawking's small books), at least when I was 8 or 9. My cabinet also had a book on Geometry; I still have that,
But what constitutes a perfect cabinet of curiosity? I don't know, but I guess in ancient times, or perhaps medieval, when kings and connoisseurs were making their cabinets, they included many precious things in them. We can't imagine even finding some of them now as they were exquisite in that period. I recommend you read some articles and books on it. Kings of those times were likely to build one hall or building to showcase what they had. Now, what they had is a different matter, but what to emphasize is that we have lost its culture. Though people, often academians, build a library that contains only books. I know some people who like to collect paintings, and their house is just paintings by artists like Van Gogh. I haven't seen any theatre of curiosity, and I hope to see it soon.
Curiosity is different for different persons. It pushes us to know what we can't, and I assume many have this definition in their books. However, some believe it to be a pause for us to stop searching. Curiosity doesn't mean you have to find what is to be found; you have to find what you want to find, which is the classic definition. Some doubt, in philosophy, how much curiosity is good. I have no idea; curiosity is not an entity of quantity, so how can we put an upper or lower bound on it? Curiosity is nothing if tied to the environment, and hence environment is the key to the 'subject' for defining what lies beyond curiosity.
An important thing to note is that there is a sentence in literature, "curiosity killed the cat," so we better not pry much and call it curiosity. Some works can be done without curiosity, and some need them badly. Science falls in the latter category.
Amid the tensions anent many things, of which, the most destructible is COVID. I recall some verses from a book I read.
THAT I WANT thee, only thee-let my heart repeat
without end. All desires that distract me, day and night, are false
and empty to the core.
As the night keeps hidden in its gloom the petition for light,
even thus in the depth of my unconsciousness rings the cry-I want thee,
only thee.
As the storm stills seeks its end in peace when it strikes against
peace with all its might, even thus my rebellion strikes against
thy love and still its cry is-I want thee, only thee.
However, it can be interpreted that it was written to call some divine power. I interpret it differently. I just had a feeling to share this awaken poem, and you are allowed to search for the poet who wrote these beautiful verses.
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
People are often heard whispering "Tit for Tat", but reciprocally. Yet, what is the game theory behind Tit for Tat (TFT)? For that, what is TFT?
TFT is the usual game for two/more individuals or two/more groups. It starts with a situation where one of the teams is given a chance to first act. This act can be of two types, either defection or cooperation. Then the second player acts according to the previous move. The most classic and well-known example is Chess. When white moves its piece, the black always makes a move according to the first. But this is not always right. In chess, if a move doesn't concern you much, you can follow your lead using your strategy without being in a situation where you have to act accordingly.
However, there is one fascinating game theory called the Prisoner's Dilemma, which uses TFT (and its extensions) very much. It is intricate at first but self-realizing after you allow the logic to play itself. Merrill Flood and Melvin Dresher were the first ones to realise this game. Afterwards, Robert Axelrod influenced this game theory.
Prisoner's Dilemma is a situation concerning the two criminals who are arrested. Let's say A and B are criminals. Just for the sake of game theory, we give both the criminals a chance to get free from charges. Conditions are that A and B are given two choices. These choices are imagined on a ground where both are standing with each other. The options are to either defect/betray the opponent or remain silent. The catch is, they are not allowed to talk or get informed about one another. Rules are as follows,
It is very wondrous and naive to think of the Philosophy of Science as not a part of Science. It is merely innocence. From Socrates to Russell, from Newton to Dyson, everyone intelligently used this philosophy as a weapon to turn down the disturbances and get the very thing they wanted. In fact, intellectuals used this in their private life too.
By definition, Philosophy of Science seems nothing but an old-school study. And that deceives the overall person pursuing science to think relatively modern. And by modern, we mean something extraordinary. However, in quite a sense, remarkable and unparalleled are basically locations inside philosophy. But going through the works of Kant says nothing, I mean supposedly, about the cultural science. This cultural science is nothing but the experimental science that is usually derived from theoretical works.
Here, Kant (1) is talking innocently about physics, and if we agree to a point, then we might lose the other point we were holding then. And yet if we are not satisfied, we are in a state of war with ourselves. However, if we are adequately met, we defeat a so-called monstrous idea. However, the outlandish idea is still a golden idea for someone else.
Conclusively, philosophy tells us much about War (2). However, this war is not dangerous (until a political angle jumps in), because it is some ideological war. And if we patiently derive what we would gain, then it would be some answers and confusions: Technically, both. The philosophy of science teaches us the importance of doing science, not just cultural science (or empirical), but also the science that deserves to be studied. While doing so, the individual must not be deceived by evils' ideas, otherwise, the person would be paralyzed in a peculiar non-cultural and baloney science.
References and Footnotes
1) Citing Immanuel Kant works, such as Critique of Pure Reason, Critique of Practical Reason, etc.
2) It is quite an educational war.
