Early the next morning, Qiao Yu had breakfast and walked leisurely towards the library.

Passing by the playground, Qiao Yu stopped to look at it for a while.

A group of young juniors and girls are undergoing military training. Well...wait a minute, if he goes to school at the age of six, these young people undergoing military training seem to be the same age as him, and most of them may even be older than him.

Thinking of this, Qiao Yu felt a little unhappy.

There is indeed no fairness in this world.

Obviously everyone is the same age, so as long as these juniors and juniors study casually, they can get relatively good results and get good grades.

The rest of the time they can enjoy life. They can choose to fall in love with each other; they can join various clubs to develop their interests and hobbies while expanding their social circle; they can also sign up for exchange students...

No one puts pressure on them, no one even cares about them. They have a colorful college life and can do whatever they want!

But he is different.

Every day when you open your eyes, it's scientific research, scientific research, scientific research. If you slack off a little bit, the instructor will pull him in and give him a beating.

Not only that, he also has to be busy with his own career. Chief Engineer Yu calls him every day, just like saying hello...

Mingming Xiaoyu Technology's servers are ready for computing. Although there are still some minor problems, Senior Brother Chen's lover is in charge and still bothers him every day.

Fortunately, Qiao Yu knew who the culprit was...

It's all Frank's fault!

If it weren't for this irresponsible man, he would probably be able to live like these juniors and enjoy a wonderful youthful life instead of carrying the burden of life on his young shoulders.

Thinking of this, Qiao Yu wanted to make life more difficult with Frank again. He had to look back and find out what direction this guy had chosen to re-choose as a subject...

This is not difficult.

After all, he is now a Fields Medal winner, has a rising reputation in the international academic community, and has many friends in the international mathematics community.

When the time comes, you should find some excuse to express your concern for Professor Frank and you should be able to get some information.

He is not afraid at all that his relationship with Frank will be exposed. If he is born but not raised in any relatively civilized system, there will be no support from public opinion.

Walking to the library in low spirits, Frank had once again been transformed into thirty-six different appearances in his mind.

There are not many people in the library during the holidays, but there are quite a few.

Many graduate students also need to search literature, especially graduate students in the social and humanities fields. They spend most of their time searching and reading various literature materials.

There is nothing we can do about it.

For example, the well-known history department of Yanbei University cannot allow historical scholars to invent and create history.

All research can only look for clues in the vast variety of historical records. Its value can only be reflected in the excavation and interpretation of historical truth.

There is no need to go to the laboratory, so naturally you can only go to the library.

As for Qiao Yu, the purpose of coming to the library is to find some literature on quantum physics.

Since we are going to do quantum computing simulations, studying quantum physics is naturally an indispensable learning content.

Different from the research methods of ordinary people, what Qiao Yu wants to do today is critical research.

For example, functional analysis, quantum Fourier transform, etc., and of course Hilbert space.

After all, in the mathematical framework of quantum physics, Hilbert space is almost indispensable.

Whether it is the representation of quantum states, the operation of operators, or the construction of measurement theory, Hilbert space plays a crucial role.

The reason is also very simple: in quantum mechanics, the possibility of quantum states is infinite, which determines that the inner product space in which it resides must be infinite-dimensional.

As we all know in mathematics, if a parameter goes to infinity, while all physical states must still remain within the defined space, then this means that the space needs to be complete.

That is, the limit of any convergent sequence still belongs to this space. This characteristic corresponds to the completeness requirement of Hilbert space in functional analysis.

However, from Qiao Yu's perspective, Hilbert space has too many shortcomings.

The first is the issue of physical interpretability. Quantum states are vectors in Hilbert space, but actual measurements can only obtain probability distributions, rather than directly obtaining vector information.

At the same time, the problem of wave function collapse is not strictly mathematically described in Hilbert space. You also need to refer to the Copenhagen interpretation and other explanations.

Facing infinite-dimensional problems requires infinite-dimensional Hilbert spaces, and mathematical operations on these spaces require facing a lot of difficulties.

For example, scattering states require the help of Lie operators, and vacuum fluctuation problems in quantum field theory require mathematical tools such as distribution theory, which are beyond the scope of traditional Hilbert space.

Other issues include measurement and non-locality, and the incompatibility between gravity and quantum mechanics. Most importantly, Hilbert space is also incompatible with the random matrix tools he needs to use...

In short, Qiao Yu simply couldn't imagine how people in mathematical physics could tolerate a core mathematical tool for describing quantum systems that was so difficult to use.

He had not done research in this area before, so he didn't mind what tools these people used. But now that he was going to start doing research in this area, he naturally had to upgrade the tools.

After all, even the ancient Chinese understood that if a worker wants to do his job well, he must first sharpen his tools.

In this way, Qiao Yu found a pile of books in the library, started to flip through them quickly, and then referred to his notes to start thinking about what improvements were needed in the new space framework compared to Hilbert space.

Of course, this spatial structure is still based on the generalized modal axiom system. After all, even those foreign mathematicians and physicists have seen the advantages of this system, and Qiao Yu naturally cannot fail to see it.

According to the new mathematical framework created by this system, it is necessary to avoid the probabilistic interpretation problem of Hilbert space, and it must also be able to solve non-locality problems and allow finite-dimensional approximations.

At the same time, it is necessary to upgrade to modal arithmetic algebra to solve the infinite-dimensional operator problem and optimize the measurement theory. The ideal state is to be automatically compatible with quantum field theory.

In addition, measurement issues must be taken into consideration, and it is best to be able to perfectly describe the quantum field. This can be directly applied to the study of quantum gravity and avoid the incompatibility problem of Hilbert space.

At the same time, it also allows the study of the topological evolution of high-dimensional quantum states, which is no longer limited by the spatial dimension.

In this way, the subsequent work does not need to endure the various defects of Hilbert space.

Yes, although there has not yet been a final answer on whether the project will pass the approval, Qiao Yu has already started making preparations.

Anyway, he does not need the cooperation of others for these purely mathematical theoretical work.

After reading the literature for two hours.

Qiao Yu opened the paper editing software on his computer and first wrote a title for his current research.

“Topoloization of Quantum States Under the Generalized Modal Axiom: Construction and Applications of the Qiao Yu Quantum Modal Space“

Translated into Chinese is "Quantum State Topology under the Generalized Modal Axiom System: Construction and Application of Qiao Yuan Quantum Modal Space".

Yes, Qiao Yu unceremoniously named this new system after himself.

Although Hilbert did not do this at that time, he only proposed the concept of a complete inner product space, but the name of Hilbert space was given by later generations based on his research.

However, Qiao Yu felt that this was because Hilbert had not perfected the entire space system at that time.

For example, the completeness of L space was proved by Reese in 1912. It was not until 1927 that the famous John von Neumann officially introduced the term Hilbert Space.

But his situation is different. Because he can completely prove the completeness proof of Qiaoyu modal space by himself. He can also directly prove the various advantages over Hilbert space, and there is no need for future generations to improve it.

So there is no problem for him to name it after himself. As for this, it seems immodest...

That’s right!

After browsing around on the Internet yesterday, Qiao Yu felt that it was necessary to correct some foreigners' stereotypes about Chinese people and change the traditional inertial thinking of the older generation.

Being humble is what you need to do when you don't have the strength. If he is still humble when he is already so powerful, isn't that saying he is powerful in vain?

Don’t you feel comfortable naming the complete space system I created by myself? Then just don’t use it when doing related research in the future.

I can't help it, I'm just so domineering.

Not to mention those foreigners, as long as his mentor, grandpa and mother were not around, Qiao Yu felt that no one could control him.

Of course, every young person may have this illusion at some stage, and even Qiao Yu it is not serious.

A truly rebellious teenager dares to be lawless even when his parents are around him, and he is no bigger than him.

If you take into account Qiao Yu's background, no matter where he is in the world, he can be regarded as a person with both good character and academic excellence.

When Qiao Yu started to write down his thoughts, the phone suddenly rang in his pocket.

Because of the recent popularity, Qiao Yu specially wore a mask and chose a corner seat in the library study room. He was just afraid that it would be too troublesome if he was recognized.

Who would have thought that forgetting to mute his cell phone would directly make him the most handsome and most watched kid in the study room.

When people glanced in his direction with a hint of disgust, even a person like Qiao Yu who didn't care much about other people's strange looks couldn't stand it.

Well, the main reason is that the moral bottom line is too high.

So Qiao Yu quickly took out his phone, glanced at it, hung up the phone, put his phone into do not disturb mode, closed his laptop, stood up and walked out of the library.

Hey, Director Tian really didn’t know how to give a warning before calling.

…

After walking out of the library door, Qiao Yu took out his cell phone and dialed Tian Yanzhen.

Sure enough, just as he walked out, Director Tian called him again.

As soon as the call was connected, before he could speak, the other person asked: "What are you busy with? Why is the phone still hanging up?"

"In the study room of the library, there were quite a lot of people just now. I'm sorry to answer the phone, Director Tian."

"What are you doing in the library? Aren't you clamoring for your own exclusive study room every day? Isn't it enough for you to take away so many of my books?"

"Look for some information and literature on mathematical physics and quantum physics. Isn't this a promise to you? I will work hard on the project when I come back. I must keep my word."

This reason is impeccable.
To be continued...