From all-round academic master to chief scientist

Existence problem of Yang-Mills gauge field?

Looking at the mathematical formula Lin Xiao wrote on it, the physicists present reacted. After all, this is what theoretical physicists like them have been studying.

Of course, mathematicians also reacted later. In any case, although this problem belongs to physics, since it is included in the seven major millennium mathematical problems, for these top mathematicians, even if they do not know If you study it, simply take a look and understand something, you will still be able to do it.

So at this moment, the scientists present were extremely puzzled by what Lin Xiao was doing at this time.

What is this going to do?

Didn't he just finish narrating that paper last moment?

Shouldn’t it be time to ask questions next?

Although the people present had understood how his method came about through Lin Xiao's explanation, they still had some questions about the entire paper, so many people were planning to ask questions.

Why did Lin Xiao turn around and write this?

Everyone present couldn't help but have an unbelievable guess in their hearts. Could it be that Lin Xiao also wanted to solve this problem during this report?

"Witten, you should know what's going on, right?"

In the seat below, Maldasi had a serious face. While watching Lin Xiao's next steps, he asked Witten next to him.

He recalled what Witten said when he and Witten chatted before the report began, and asked in great surprise: "Don't tell me, this is the surprise Lin wants to give us? No, it should be a big surprise?! "

Witten laughed and said, "Let's just look down. For now, I can only tell you that this is just a surprise, not a big surprise."

"Isn't this a big surprise?" Maldacena said it was hard to believe. If this is not a big surprise, then what is the big surprise?

Proving the existence of the Yang-Mills gauge field is definitely a major event in their theoretical physics world. Although it is not comparable to the unification of quantum mechanics and relativity, for many physicists, this is still a big deal. Huge significance and role.

After all, this question is about the strong interaction, and there are so many physicists studying the strong interaction, and there may be quite a few physicists who are excited by this matter.

So, what is the bigger surprise than this?

Maldacena naturally thought of the problem behind this problem, which is the quality gap problem.

"You mean, in addition to this proof of existence, does Lin also need to solve the mass gap problem?"

Hearing Maldacena's guess, Witten just smiled slightly and did not answer. Instead, he pointed at Lin Xiao above and said, "Just keep reading, it will only take an hour or two."

Looking at Witten's appearance, Maldasi felt itchy in his heart. Although it was indeed only for an hour or two, how could he endure this kind of thing just because he wanted to?

But when he looked up and saw Lin Xiao's next steps, his attention was immediately attracted.

"This...is this?"

He widened his eyes and looked at what Lin Xiao wrote at this time.

"Is this a derivation that directly uses the conclusion of the unification of relativity and quantum mechanics?"

In an instant, he put his mind into it. At this time, the method used by Lin Xiao in the proof process will provide certain theoretical guidance for the subsequent research of physicists like them, especially in mathematics. guide.

So even though Maldacena felt very itchy in her heart, she also started to look at it seriously.

After all, in terms of mathematics, although he is quite confident, he still has to learn from Lin Xiao, a top mathematician who has won the Fields Medal and the Wolf Prize in Mathematics.

Of course, it wasn't just him. Even Witten, who also won the Fields Medal next to him, also watched Lin Xiao's process seriously.

Although he knew that Lin Xiao had proved this problem, he had not seen Lin Xiao's proof process, so when he saw Lin Xiao's proof at this moment, his eyes could not help but light up and he felt a certain amount of inspiration. .

As a result, everyone in the audience quietly watched Lin Xiao's performance on the stage. Everyone fell into silence, and no one spoke.

Although the students present who came to watch did not know what happened, after all, most of them could not even understand a formula written by Lin Xiao on the blackboard, but at this moment they also knew that their master Lin Probability has done something incredible again.

In this way, as time passed, Lin Xiao wrote more and more things on the blackboard, and the same things became more and more complicated.

When one blackboard was used up, another blackboard was replaced. Even after the replacement, Lin Xiao did not open his mouth to explain, but just wrote on his own.

Of course, because of this, there are fewer and fewer people who can keep up with him.

Even some famous physicists, even Nobel Prize winners in physics, need a certain amount of time to think, but before they can think about it, Lin Xiao has already written the next step.

This made them feel helpless. Why did they write so quickly, without saying a word, and without giving them any time to think?

But you can't just look up and wait. If your friends find out when the time comes, they might guess that you didn't understand Lin Xiao's steps. Then you won't be laughed at by your friends later?

So they endured the pain of not being able to keep up and let their brains run to the extreme to keep up with Lin Xiao's calculations.

In this way, the thousands of spectators in the huge Beijing University Auditorium, almost full of seats, seemed to be watching a mime for a moment, and the only protagonist of this mime was Lin Xiao on the stage, and the hand in his hand. of chalk and the blackboards.

Twenty minutes passed, and Lin Xiao also wrote on the blackboard for half an hour.

The handwriting stopped in the middle of the fourth blackboard. The four filled blackboards were filled with dazzling mathematical and physical symbols.

More than 99% of the people in the audience had expressions of "It's finally over", while the remaining less than 1% had expressions of "I see."

The proof of existence has been completed.

The remaining less than 1% of people are all those who can keep up with Lin Xiao's thinking. At this time, in addition to being amazed that Lin Xiao has achieved this, they sincerely admire Lin Xiao for doing this.

Lin Xiao had just completed the unification of quantum mechanics and the theory of relativity, but was able to use it in the next proof in a blink of an eye. This ability to integrate everything was something they could not learn no matter what.

At this moment, Lin Xiao also spoke: "I'm sorry, everyone, I kept everyone waiting for so long."

His voice broke the continuation of the mime, and at the same time made the people present turn their attention to him again.

"I know that everyone may be wondering why I suddenly want to study the relationship between gravitons and relativity, and why I suddenly unify quantum mechanics and relativity."

"Actually, these purposes are for what you see, yes, it is the existence problem of the Yang-Mills gauge field."

Lin Xiao smiled, and then continued: "Haha, to put it this way, the unified theory of relativity and quantum mechanics is just to solve such a problem, but it is a bit... well, how can I put it, killing a chicken with a bull's-eye? Haha, no Having said that, when I was solving this problem, I didn’t think too much about it, I just thought about it, and then I did it, and in the end, I accidentally succeeded.”

The people below immediately rolled their eyes wildly.

We know you are awesome, but is now the time to talk about this?

Isn't it about another issue?

The problem of the Yang-Mills gauge field is divided into two parts, and the most critical problem is the mass gap.

The combination of these two problems is a complete millennium problem.

As for which of the two questions is more difficult... the people present don't know, after all, they have never done it.

However, Lin Xiao did not disappoint them.

"Of course, everyone must be aware that there is another problem with the Yang-Mills gauge field."

"That's the quality gap issue."

"To be honest, I haven't solved this problem yet -"

When Lin Xiao said this, the physicists present showed regretful expressions.

It seems that they cannot witness the second history today, but only 1.5 histories.

Witten underneath also showed a look of regret, as if the big surprise was gone...

But it is understandable. After all, there is only one day from yesterday to today. It is entirely possible that Lin Xiao has not solved it.

But, what about the surprise Lin Xiao said she wanted to give him?

Just when he was confused, Lin Xiao on the stage said: "However, at this report meeting, I want to challenge myself to prove the existence of the quality gap on the spot!"

The people present who had just felt a little regretful were once again shocked by Lin Xiao's words.

Challenged to solve quality gap issues on the spot?

"Is this something that can be done?"

Everyone present had such a question in their hearts.

This is not as easy as Lin Xiao's two conjectures in the report.

Although asking questions and solving problems are both important, they are obviously different in terms of difficulty!

Witten was also surprised. Is Lin Xiao sure he wants to do this?

He believed that Lin Xiao must have a certain idea, but it was not impossible for him to be stuck on a problem for ten days and a half, or even three years and five years at the last moment.

And if Lin Xiao fails in the challenge, doesn't it mean that he has revealed his ideas? It would be bad if others knew his ideas and completed the proof first. In fact, this matter is not good. Not that it hasn't happened.

Even when Perelman proved the Poincaré conjecture, he encountered this kind of thing. At first, because Perelman's proof was too concise, many people couldn't understand it, which led to the theft of some people. I want to create a more perfect version according to Perelman's ideas and take away this honor.

And now Lin Xiao will undoubtedly face this situation.

Of course, others were thinking the same thing at this time.

Professors from the School of Physics and the School of Mathematics at Beijing University were anxious.

Although Lin Xiao has not proven it now, maybe it will be proven in a while?

And if he shares his ideas now and this "challenge" fails in the end and others take advantage of him, it will be more of a loss than a gain.

If Lin Xiao proves it, then the news will be [Professor Lin Xiao of Peking University School of Mathematics (School of Physics) has successfully proved a world-class problem].

However, no matter how anxious they were, they could not stand up to stop Lin Xiao at this time, and it was impossible for them to regard Lin Xiao as some "ignorant junior" or "innocent subordinate".

At this moment, Lin Xiao had already picked up the pen and started writing on the blackboard.

[φ(0,t)φ(0,0)~∑Anexp(-nt)…]

Seeing Lin Xiao's actions, the physicists and mathematicians from abroad were heartened and began to cheer up. The professors from the School of Physics and the School of Mathematics sighed helplessly, forget it, just I can hope in my heart that Lin Xiao can really complete the proof.

On the other side, Maldacena couldn't help but sigh: "It was only then that I remembered that our Professor Lin is still a young man. This can almost be called an impossible challenge, and probably only Lin Professor, do you dare?"

Witten shook his head slightly, "Maybe it's because of his youth, but I think it has more to do with Lin's talent. In fact, yesterday, I saw that Lin had actually proved the first existential question, and He just started taking action when it came to the quality gap issue."

"What?"

Upon hearing the news from Witten, Maldacena immediately felt incredible.

Yesterday, Lin Xiao actually started to prove the quality gap problem?

But when he was about to ask for some details, he saw Witten suddenly looking up with a look of surprise and a little joy.

Maldacena raised his head in confusion and didn't see anything, but Witten's expression told him that it didn't seem that simple.

But in fact, Witten made such an expression because he received a surprise from Lin Xiao.

That is the mathematical derivation that Lin Xiao is writing.

Lin Xiao's mathematical derivation method at this time is somewhat similar to the mathematical derivation methods he provided to Witten in the past, but the method at this time is more direct to the essence.

This is of great significance to Witten's goal of finding the existence of strings.

Therefore, he was extremely surprised, and he paid more attention than before, carefully watching Lin Xiao's proof process, and at the same time, he was still analyzing in his mind the thoughts reflected in Lin Xiao's methods.

At this moment, he even had the idea that he might have to stay here for half a month to discuss with Lin Xiao.

Of course, after seeing the mathematical method used by Lin Xiao, others present gradually discovered the subtlety of this method. Undoubtedly, this is a method that is very suitable for use in mathematical physics research.

This made everyone present couldn't help but sigh, this guy has shown dazzling mathematical skills, and now he can create this kind of mathematical method.

"Where is this guy's limit?"

At this moment, Lin Xiao on the stage did not look at the reactions of others, but completely sank into his own state.

Because he only completed this part of the derivation process in the past two days, it was impossible for him to recite it backwards and forwards, so now he is completely re-derivating it.

However, re-derivating is not difficult for him. A top mathematician like him can re-derive all the processes and results in some papers just by looking at the abstract, so this step is quite simple.

But the key question is how to complete the final problem.

From yesterday to today, he has been stuck on the last problem for a long time. It seems that he is very close to success, and he is just one step away from success. But if this kick cannot be taken, everything will be in vain.

And he will also become the most generous person in the history of physics, because he selflessly revealed all the ideas on such an important issue.

But obviously, he didn't want to be the most generous person.

So he was writing the previous derivation on his hand, but his mind was running almost at full capacity, thinking about where the proof of the final problem should be. And with the development of his brain, he was processing every second in his mind. The "data" of people is almost ten times that of ordinary people.

"Of course, we can't forget to thank the sun."

Suddenly, Lin Xiao smiled. It was that beam of sunshine that allowed him to find his final direction.

Another fifteen minutes passed, and he had already explained all the derivation processes leading up to the final question.

At this time, his handwriting stopped at the last "∑" symbol.

Everyone present was silent, looking at Lin Xiao's right hand that stopped.

Is this the end?

Those top physicists and mathematicians who have followed Lin Xiao's thinking have already seen that Lin Xiao has reached the last level. As long as he solves the problems at this last level, he will succeed.

But Lin Xiao, is he stuck at this last level?

If this is the case, everyone present can't bear to look at it. If Lin Xiao can't take the lead in solving it by himself in the end, then he will be the real ultimate wage earner.

But at this moment, Lin Xiao suddenly turned around with a smile on his face.

That smile shocked everyone present, didn't it?

“The color confinement property of the non-commutative group Yang-Mills theory has been proven in line with the rigor of theoretical physics, but there is no proof in line with the rigor of mathematical physics.”

At this moment, Lin Xiao spoke.

"In other words, beyond the confinement scale, those color-charged particles are connected by the 'flow tube' of chromodynamics, so there is a linear potential between the particles, so free color-charged particles such as gluons cannot exist."

"And if there is no such confinement effect, we should see zero-mass gluons; but because they are confined, we can only see the bundled state of gluons without color charge - glue waves. All glue waves have mass, so we expect The existence of quality gaps.”

"However, in the past, we have only achieved rigorous proof from experiments. We can completely see this from the "area law" of the decline in the vacuum expectation value of Wilson's circle. However, we still lack mathematical proof."

"Because only through rigorous mathematical proof can we deduce this result more accurately."

"And this is when we need to start with photons."

Everyone present was stunned. Lin Xiao had said so much, but finally came to Photon?

But at this time, someone quickly reacted, such as Maldacena.

His eyes were shocked, "Yes, photons! If it is a photon, this mathematical model will be..."

"Photons don't seem to have anything to do with the strong interaction, but friends, we have to remember our purpose again, which is unification."

"And now, I think I've found an opportunity."

Suddenly, Lin Xiao turned his head and added the formula representing photons to the final mathematical model of the strong interaction.

At this time, the mathematical derivation that originally seemed to be impossible to proceed suddenly underwent another transformation and formed a completely new form.

Everyone in the audience already knew what Lin Xiao was going to do next.

Next, Lin Xiao easily deduced this new formula.

till the end--

"So here, we can easily prove that if it is greater than 0, there is a mass gap!"

"At this point, everything is clear - the Yang-Mills gauge field exists and meets the strict standards of contemporary mathematical physics, especially constructive quantum field theory. At the same time, the mass of all particles in the force field predicted by the theory is strictly positive. of."

"The mystery of the strong interaction will be revealed to physics from now on, and its mysterious veil will be unveiled."

After saying that, Lin Xiao opened his hands to celebrate the success of his challenge.

The audience also burst into applause to celebrate the winner.

Two chapters combined into one