Xueba starts with change

Chapter 562 Mathematics①

"Eigenvectors and eigenvalues..."

After downloading a batch of documents, Chen Zhou couldn't help frowning, and silently recited these two keywords.

Even though this is Chen Zhou's favorite research method, there are too many literatures found on the computer, right?
With just these two keywords, Chen Zhou found a large amount of literature on the preprint website e-Print arXiv.

While this speaks to the power of the preprint site e-Print arXiv, it also speaks to the extensive research of the underlying mathematics.

However, this is not what Chen Zhou wants!
Chen Zhou had to sift through the massive amount of documents he needed, and then download them.

For Chen Zhou, it was too time consuming.

Involuntarily, Chen Zhou thought of Zhang Yifan and the subject of the 43 Institute that year.

"Sure enough, it's good to have someone to help prepare the materials..."

Chen Zhou sighed with emotion in a low voice.

Immediately, Chen Zhou thought of his 4 assistants, and his students who hadn't registered yet.

He figured that if he encountered such a situation again in the future, he would definitely have to make some arrangements.

Anyway, now he has no shortage of people.

Furthermore, Chen Zhou would feel ashamed if students were not allowed to do things like this that help students grow.

Thinking of this, Chen Zhou's mood also improved a little.

Refocusing his attention on the computer screen in front of him, Chen Zhou began to sift through the pages of documents.

During the selection process, Chen Zhou was also thinking about adding new keywords.

Since you can't order others, you can only find a way by yourself.

Otherwise, if there are so many documents and materials to be screened one by one, he should not do this subject.

As time went by, Chen Zhou's speed of screening documents was also gradually accelerating.

On the one hand, it is because of the addition of new keywords.

On the other hand, it is because Chen Zhou discovered the pattern of these mixed documents on the preprint website e-Print arXiv.

Now he can distinguish between good and bad documents without having to click through one by one.

Download the documents that are useful to him and that he needs.

But this is a time-consuming process after all. Chen Zhou still spent a lot of time in the process of searching and downloading documents.

After downloading a document again, Chen Zhou looked at his watch and temporarily stopped searching and downloading the document.

He had to turn to the embrace of topics related to neutrino oscillations.

But what Chen Zhou didn't know was that it wasn't long after he uploaded the research paper on the minimal model program to the preprint website e-Print arXiv.

The number of visits to this website began to rise sharply.

At one time, the management personnel of the website thought that the website had been hacked.

After analyzing the background data, they were relieved.

These increased visits are all directed at a newly uploaded paper.

It's just that while they are relieved, they are also curious.

What kind of paper can attract such a large amount of traffic?

Moreover, this is obviously a paper that has just been uploaded not long ago, why did it attract so much attention in such a short period of time?
Out of curiosity, the managers of the website also found this newly uploaded paper.

When they saw the author's name on the paper, they were not surprised immediately.

I also instantly understood why these sudden increase of visitors were so excited.

After all, in the current mathematics world, which mathematician's attention can be compared with that young mathematician from Huaguo?

The managers were right.

The sudden and sharp increase in the number of visits to the website was precisely because the news of Chen Zhou's uploaded thesis was spread.

Then, it attracted a large number of followers.

The number of downloads of Chen Zhou's paper "Studies on Minimal Model Program and Z-Theory" is also increasing at an extraordinary speed.

In fact, Chen Zhou did not even think of this point.

Because in his opinion, there are not many mathematicians who conduct research on the subject of the minimal model program.

Then, on the preprint website e-Print arXiv, naturally there will not be many people who follow the research trends in this field.

Therefore, when Chen Zhou uploaded the thesis, he was thinking that his thesis would probably not be noticed by many people.

If you want to really enter people's field of vision, you probably need to wait until the latest edition of "Annual of Mathematics" is published.

However, what Chen Zhou didn't think about was.

There are indeed not many people who pay attention to this research field.

But there are not many people who pay attention to him.

When he uploaded the news of the paper, he notified everyone who followed him in the form of a newsletter.

The attention of his paper suddenly increased.

Even, in the following period of time, the degree of attention in the field of the minimal model program remained high.

On the preprint website e-Print arXiv, every once in a while, a large number of papers on the program of extremely small models and further research appear.

To quote Terence Tao, it was Chen Zhou who single-handedly brought the attention of mathematicians all over the world back to this forgotten field.

Of course, Chen Zhou, who is currently concentrating on neutrino oscillation-related research, does not know what happened on the e-Print arXiv website.

After the minimal model program was solved, the research on neutrino oscillation related topics became his only adjustment between searching literature and downloading literature.

Interestingly speaking, the current Chen Zhou even felt a little bit of joy when he saw these familiar contents.

It can only be said that the screening and downloading of a large number of documents really made Chen Zhou feel boring and boring.

However, it was necessary to find the answer to his strong feelings.

This is also an objective situation that inevitably exists in the process of academic research.

Compared with other scholars, Chen Zhou is fortunate that he was able to obtain certain feedback from the beginning of his academic research.

Unlike most scholars, who seem to be groping forward in the dark, no one knows what kind of scene is ahead.

It is precisely because of this that while rejoicing, Chen Zhou worked hard to change himself.

"Theoretically speaking, before jumping out of the standard model, neutrinos belong to fermions, and the neutrinos of the three flavors are also different from the three generations of charged leptons, forming an isospin double state..."

"The non-conservation of parity in the weak interaction also shows that the neutrinos participating in the weak interaction are left-handed, and there are no right-handed neutrinos..."

"From the two-component neutrino theory proposed by Mr. Yang and others, and the Weinberg-Salam model describing the weak interaction, it is shown that there are only left-handed neutrinos and right-handed antineutrinos..."

"And the intrinsic spin of this neutrino determines its mass to be zero..."

"This also corresponds to the standard model. If there is no right-handed neutrino, the mass term of the standard model interaction Lagrangian, the mass term of the neutrino is zero..."

"This also means that neutrinos are strictly massless in the standard model..."

Chen Zhou tried to think about the mass of neutrinos again from the perspective of the Standard Model.

The multi-angle thinking of a subject is also a research method that Chen Zhou likes to use.

Because, only by clarifying the original logic of the problem, can we discover the real problem in the subject and solve this problem.

Chen Zhou also discovered at this time that the standard model's restrictions on neutrinos are a bit too rigid.

Because the standard model theoretically predicts that there is mixing, or oscillation, among the three generations of quarks, and its mixing matrix is ​​unitary.

However, the conservation of lepton number guarantees that there is no mixing between the three generations of neutrinos.

That is, neutrino oscillation does not occur.

Therefore, any experimental evidence that neutrinos have mass, or can oscillate, would indicate new physics beyond the Standard Model.

But the reality now is that neutrino oscillations do exist.

The new physics beyond the standard model also exists with a high probability.

Thinking of this, Chen Zhou smiled softly.

He remembered something a physicist had said.

The Standard Model is nothing more than the patchwork state of physics.

Now Chen Zhou can somewhat understand the meaning of this sentence.

Withdrawing his thoughts, Chen Zhou picked up a pen and continued to study on the draft paper.

Speaking of which, the proposal of neutrino oscillation itself is also based on the standard model.

In the standard model, the left-handed and right-handed parts of charged leptons and quarks are coupled through the Higgs scalar field to obtain mass.

Therefore, if this mechanism is extended, the right-handed neutrino field is introduced, and the same method is adopted, neutrinos can also have mass.

However, this generalization cannot explain the neutrino mass, which is much lighter than other fermions.

Therefore, in 1958, Italian physicist Pontikov pointed out that if the mass of neutrinos is not zero, neutrinos of different flavors can be transformed into each other.

That is, oscillation occurs.

It can also be seen from this that any theory needs to withstand constant testing.

Even that theory has been recognized by countless people.

There are always people who will come up with different perceptions.

This is also the trajectory of the development of human science history.

[Assumption 1: There are no right-handed neutrinos and left-handed antineutrinos. 】

[Assumption 2: Lepton number conservation. 】

Chen Zhou wrote down these two assumptions on the draft paper.

These are also the two assumptions required to obtain the conclusion that neutrino mass is zero in the standard Weinberg-Salam SU(2)×U(1) electroweak unified theory.

Once one of these two assumptions fails.

Then, neutrinos can gain mass.

[According to the standard model, left-handed charged leptons and neutrinos constitute a double state, but because charged leptons have mass, they have two states, left-handed and right-handed. 】

[Therefore, the Dirac quality mD is naturally produced, that is, LD=mDφφ...]

Looking at the formula he wrote on the draft paper, Chen Zhou habitually picked up a pen and clicked on the draft paper.

Because of this mass item, what is guaranteed is the lepton number conservation.

But the situation with neutrinos is not the same.

Neutrinos are electrically neutral, unlike charged leptons and quarks, which have an electric charge.

Therefore, neutrinos do not have Dirac mass.

But in the grand unified theory, right-handed neutrinos also exist.

In this case, neutrinos should also have Dirac mass.

After thinking for a while, Chen Zhou marked the words "Dirac neutrinos" behind the formula.

Then, a horizontal line was drawn in the middle of the draft paper.

Below the horizontal line, Chen Zhou continued to write:

[Because neutrinos are electrically neutral, according to the Lorentz invariance, neutrinos can have Majorana mass mM even if there are no right-handed neutrinos, that is, LM=mM(φCφ+φφC). 】

[Where φC is the charge conjugate spinor, through the action of LM, neutrinos and antineutrinos can transform into each other, thus destroying the conservation of lepton number...]

After finishing writing, Chen Zhou also marked the words "Majorana neutrinos" behind the formula.

Two kinds of neutrinos correspond to two hypothetical conditions respectively.

In other words, as long as one of them is true, then the assumptions will not be true.

The conclusion that the mass of the neutrino is zero is also untenable.

Of course, this is just the beginning of Chen Zhou's study of neutrino oscillations from the perspective of the Standard Model.

It's all just plain stuff.

But isn't that the old saying?

Well begun is half done.

Chen Zhou's intuition also told him that starting from the perspective of the standard model, it is possible to obtain different content.

Maybe it will be combined with his previous research content to give him an answer about neutrino oscillation theory.

Chen Zhou, who was thinking like this, was interrupted by the system prompt sound in his mind before he had time to continue his research.

"Congratulations to the host, you have completed the task: What is a building? It will never fall! (Continuous mathematics task)"

"Completion status: The charm of the minimal model program is something that people who are scared off by the two major problems will never be able to understand! The scenery after crossing the mountains is also a right that only a very small number of people deserve!"

"Thanks to the host for successfully solving the two major problems of the minimal model program, paving the way for the research of the minimal model program! The birth of Z-theory will also fill the gap in the research of high-dimensional clusters!"

"The host has submitted relevant papers to the journal "Annual of Mathematics". I believe that peer-reviewed mathematicians will clearly understand the importance of this paper! This is no less than the research result of Chen-Ge Theorem!"

"Completion time: From the review period to the journal publication time, it is automatically ignored. This task took 6 months and 27 days to complete. From the perspective of the project itself, it took a relatively short time!"

"Rewarded: According to the value of the host's final project paper and the impact factor of the published journal, comprehensive consideration is made, and the mathematics project conditions that are not lower than the Goldbach's conjecture level are met, and the full-level upgrade task reward is obtained once!"

After silently listening to the prompt in his mind, Chen Zhou immediately put down the pen in his hand.

Then put your chin on your hand, then close your eyes, and your consciousness entered the system space.

In the system space, the pure display screen is now filled with the content of the notification sound just now.

Chen Zhou scanned it quickly, then eagerly looked at the re-emerged personal information panel.

"Name: Chen Zhou"

"Rating: Junior Scholar"

"Linguistics Lv5 (17000/100000)"

"Natural Science:"

"Mathematics Lv8 (0/⑩)"

"Physics Lv6 (0/200000)"

"Chemistry Lv3 (0/20000)"

"Biology Lv1 (0/5000)"

"applied Science:"

"Information Science Lv2 (0/5000)"

"Medical Science Lv1 (0/2000)"

"Energy Science Lv3 (0/10000)"

"Engineering Technology Lv3 (0/10000)"

"Material Science Lv4 (0/20000)"

"Task: in progress (some tasks have been refreshed, please click to view)"

"Note: The natural science experience value balance is 108000, the mathematics level upgrade task reward is ① once, and the applied science experience value balance is 4000."

With just one glance, Chen Zhou saw the personal information panel and the note at the bottom.

The words "Mathematics full-level upgrade task reward [-] time" are really eye-catching!

With just this one glance, Chen Zhou could no longer move his eyes away...

　Thanks to book friend Yan Hongxue for the 100 starting coins!
　　Thank you book friend FYINW for the 100 starting coins!
　　Thank you for the 100 starting coins rewarded by book lovers who love reading books!
　　
　
(End of this chapter)