Great Country Academician

Chapter 537 The second solution to the Yang-Mills equation!

In the Great Hall, thunderous applause rose like a tide, and then receded like a tide.

As the applause faded, Xu Chuan took a deep breath and slowly said: "The report on the solution and existence proof of the Yang-Mills equation has been completed, and its general solution has also been verified by the Supercomputing Center. This is both for the mathematics community and This is a major breakthrough for the world of physics."

"For mathematics, this means that we can understand differential equations on a deeper level, and also gain a method that can build bridges between equations, manifolds, and geometry."

"For physics, this means that we can have a deeper understanding of the secrets of the microscopic particle world from a mathematical perspective, and even find a way to unify the three forces of strong and weak electricity."

"Of course, these are the jobs of the future, and more people will need to put in more effort."

"Okay, next, there will be a question and answer session."

"If you still have any questions about the proof report of the existence and solution of the Yang-Mills equation, you can raise it now, and I will do my best to answer it for you."

Before the words could even be finished, an arm was raised at lightning speed from the seat in the front row of the audience.

Xu Chuan looked over and saw that the person who raised his hand was the Nobel Prize winner in physics, Professor Frank Wilczek, who was also an old acquaintance of his.

Although I don't know what the problem is with this friend, but judging from the speed of his raising his hand, there must be some key point that he doesn't understand, right?

As for errors, Xu Chuan does not think there will be errors in today's report.

After all, the paper on the 'Yang-Mills Existence and Mass Gap' had passed journal and peer review in a previous life, and was accepted by the mathematics and physics circles.

After extending his hand to signal the other party to ask questions, Professor Wilzek ​​stood up, took the microphone from the staff around him, and asked a question that surprised Xu Chuan and all the scholars in the room.

"As for the Yang-Mills existence and the mass gap problem, the first half has been solved by you. I want to know whether your thinking in front of the blackboard just now about the existence of the mass gap and how to explain it mathematically, whether Already got the answer?”

Hearing this question, there was an uproar in the Science and Technology Hall.

Whispering discussions arose everywhere.

Xu Chuan was also stunned for a moment. He did not expect that Professor Wilzek ​​would ask such a question.

After being stunned for a moment, he came back to his senses and said with a smile: "No, what I am thinking about is not the problem of the mass gap, but something else."

Upon hearing this answer, Wilzek ​​was stunned for a moment. His guess was actually wrong? Have you really not thought about the problem of quality gap?

After a pause, he asked curiously: "If it's convenient, could you tell me what you were thinking about just now?"

To be honest, this question is actually a bit presumptuous. After all, there is no reason to tell you publicly at the report meeting what others are thinking about.

But for him, this was a one-thousand-meter gold bet.

Although one thousand meters of gold is not much to him, losing to others in a blind bet is not a pleasant thing, especially for someone like him who loves betting very much.

No matter what you lose, you can’t lose the bet!

Xu Chuan smiled and said, "It's not something inconvenient. If you want to know, I can write it down."

After a pause, he turned around and took out the blackboard brush from the blackboard basket, and wiped all the calculations on several blackboards clean.

Immediately, a piece of white chalk gently fell on the blackboard, and the lines of calculations came into everyone's eyes like a flowing stream.

【Rν1/2gν·R = 8π·Tν.】

[Fαβ=αAββAα+[Aα, Aβ], αFαβ+[Aα, Fαβ]= 0 】

【.】

Under the lecture table, Wilzek ​​watched curiously as the equations on the blackboard were displayed on the screen line by line simultaneously, somewhat confused.

He is not a mathematician. Although he can skillfully use mathematical tools to solve the problems he encounters in physics research, there is still a long way to go compared with those pure mathematicians.

So much so that when Xu Chuan wrote these calculations, he couldn't immediately figure out what they were through these formulas.

But just because he didn't understand it didn't mean that no one in the audience understood it.

As the number of calculations on the blackboard increased, Tao Zhexuan, who was half leaning on the back of his chair, gradually sat up straight. Until a row of core calculations appeared, his dark brown pupils shrank slightly, as if he had a premonition of something, but Some couldn't believe it.

After all, it would be amazing if it were true!

On the other side, looking at the figure writing the formula in front of the blackboard, Gerd Faltings frowned slightly and stared at the formula above seriously to calculate.

Suddenly, a bolt of lightning flashed across his heart, and a trace of surprise flashed through his brown-green eyes, staring closely at the calculation above.

If he guessed correctly, he already knew what the thing above was.

Although differential equations are not a theory he is good at, he can still see the author's thoughts and theories from those calculations.

Xu Chuan's next actions also confirmed his thoughts.

After the calculations were laid out on several blackboards, Xu Chuan threw the chalk in his hand into the basket, turned to look at the audience in the audience, smiled and said:

"The utility of symmetries is a recurring theme in the study of quantum field theory, and in many cases where precise calculations are possible, their existence is due to the existence of a non-strongest infinite-dimensional symmetry - two-dimensional conformal field theory The enhancement of conformal symmetry in China is perhaps the best-known illustration of this paradigm."

"And in the above formula I just wrote, I found a three-dimensional theory of supersymmetric fields that admits such symmetry enhancement and then performs a holomorphic topological twist."

"Relying on the micro-element construction method, a 'minimum' scalar field is set on the space-time manifold, and then under the action of the gauge group U(2)×U(1), the change is represented by the two components of the group, The non-zero asymptotic constant of its vacuum state reduces the gauge group to a subgroup of U(1)."

"In this way, we can more easily solve and obtain its general solution, and do not rely on the method of 'invariant couplers of differentiable structures set on high-dimensional manifolds'."

"This is a brand new method of solving the Yang-Mills equation. Theoretically, it will be simpler and more efficient than the previous method."

After a pause, Xu Chuan glanced at the confused audience, and then said: "Of course, what I wrote today is just a rough outline, and there are still many details that need to be filled in."

"But after this briefing, I will finish the job."

"If nothing else happens, this algorithm for solving the Yang-Mills equation will be available to everyone soon."

"As for today's report meeting, this is not the theme of it, so I did not list it at the beginning."

Under the reporting table, there was a brief silence, followed by looks of disbelief.

The audience in the auditorium looked at each other in shock, and the commotion spread from the center to the surroundings like a tide.

The second way to solve the 'Yang-Mills equation'!

How can it be? How can this be?

How could someone completely conceive of another solution in such a short period of time? This is the Yang-Mills equation, not a first-order partial differential equation or a second-order partial differential equation that high school students can do.

Even Edward Witten, as Xu Chuan's mentor, was a little shocked at this moment.

Looking at the blackboards full of calculations on the reporting table, he couldn't help but swallow, and poked G. Faltins and Pierre Deligne on one side with his hands.

"Are the things he wrote correct? There is actually a second solution to the Yang-Mills equation?"

Deligne stared closely at the calculations on the blackboard, and after thinking for a while, he said: "Although it is hard to imagine, maybe he really did it."

"This is a path that I have never thought of. Although what I wrote is only some rough things, I can still see the theories and methods behind it."

On the side, Faltings stared at the calculations on the blackboard and said nothing.

But the trace of restlessness in his eyes revealed what he was thinking.

It seems that this is not where he lost his inspiration, maybe he just took some detours.

Although many scholars who participated in the lecture were very interested in the second method of solving the Yang-Mills equation that Xu Chuan conceived at the lecture, many people also raised questions related to this new solution method during the question and answer session.

But today's report is destined to disappoint them.

Although Xu Chuan doesn't mind showing the public the unfinished theories and ideas in his mind, but now even he himself has not fully completed the second set of solutions. He has only made some basic things, so what? Can you answer these scholars’ questions?

But no matter what, today's report is destined to make waves again in the mathematics and physics circles.

Perhaps it is because the second method of solving the Yang-Mills equation attracted the attention of many participating scholars, and they could not wait for the speaker to go back and improve it;

Or maybe it was the verification by many supercomputing centers that confirmed the accuracy of the general solution and proved the perfection of the paper.

In short, Xu Chuan encountered far fewer problems than expected during the question-and-answer session.

Even, there was no need to wait until the afternoon. After the morning report meeting, the report meeting on the proof of the existence and solution of the Yang-Mills equation was completely over.

The unexpected situation also caught the Physical Society, which was hosting the conference, by surprise.

After all, they originally planned that this report meeting would last all day, so that the originally scheduled meeting process would be completely disrupted, and they had to make temporary adjustments to advance the communication report that would be held tomorrow. Come in the afternoon.

After the report meeting, Xu Chuan did not go to the noon banquet. He returned to the hotel, ordered a lunch and closed the door.

Although he had already solved the Yang-Mills equation once, when another method appeared in his mind, he was still fascinated by it.

This is not the pleasure that an answer can give, but the sharp tool he has on the road to explore the scientific wilderness, which can help him deal with the beasts that hinder the progress of human civilization;

Or maybe it's the light guided by a lighthouse that leads to the distance in the chaotic darkness.

After all, for a scholar, there is nothing more desirable than exploring the truth of the world.

Especially when you find you can do it again from a different angle.

At the same time, as scholars who came to participate in the exchange meeting posted relevant news and photos and videos on the Internet, as expected, the Internet exploded again.

【What the hell? Second solution to the Yang-Mills equation? 】

[Whose general is this person? So brave! 】

[Oh my god, I can actually find a second way to solve the Yang-Mills equation. Isn’t this a bit awesome? 】

[I seriously doubt whether he has a quantum computer brain. I suggest you cut it open and take a look! (Manual dog head)]

【Urine test! This requires a urine test! (.)ノ】

[Isn’t it just another solution? Is it worthy of your praise? 】

【? ? ? ? These are the seven millennium problems. Conjectures at the pinnacle of the human mind are not something you take a hammer to hit a nail and then discover that a steel hammer can also hit a nail. 】

[I think he may not even know what the Yang-Mills equation is, or even how to read the formula for a hundred degrees. 】

[I was shocked, I thought he could solve the quality gap problem at the report meeting! 】

[According to the speed of Sichuan God, it is estimated that the quality gap will not last long. 】

It is not only the Internet that is causing heated discussions, but also the venue where the High Energy Physics Exchange Conference is being held.

In the evening, in the spacious banquet hall of the Science and Technology Hall, many mathematicians and physicists from all over the world were walking in the hall carrying champagne, looking for their goals to chat or communicate with.

Of course, the delicacies on the table with both Chinese and Western characteristics also made many scholars linger.

Although the number of participants in the afternoon lectures and communication sessions was far less than that in the morning, there were not many mathematicians or physicists left today.

Originally, many people were planning to leave after attending the lecture on the Yang-Mills equation, but now, many people are attracted by the second solution and are ready to stay and wait.

In the banquet hall, Witten held a glass of champagne and gathered with several mathematics professors to discuss the second solution that appeared in the morning report meeting.

The reason why he is a professor of mathematics is mainly because most physicists are definitely not as good as mathematicians in mathematics. Even a top physicist like him who has won the Fields Medal has to admit this. .

In the crowd, Tao Zhexuan looked around the banquet hall with a glass of champagne. He did not see that familiar figure in the crowd.

Originally, he wanted to have a good chat with Xu Chuan about the second solution at the dinner, but now it seems that he may have to wait for a while before he can see his person.

But if you think about it from his perspective, this is normal. If it were him, he would probably choose to write the paper first before talking about it.

But I don't know how long it will take.

After thinking for a moment, he looked at Witten and Deligne and asked, "Speaking of which, when will he come out?"

These two are that person's mentors, so they should know better.

After thinking for a while, Witten said: "It shouldn't take too long. Now that he has a complete idea, it shouldn't be difficult for him to sort it out."

After a pause, he added: "The last time he solved the framework problem of the strongly correlated electronic system, if I remember correctly, it only took less than five days."

"Five days?"

Tao Zhexuan glanced at Witten in surprise. Although he didn't know much about the strong correlation electronic system, this time was too short for a top world-class problem, even if he had an idea.

Witten nodded and said: "Yes, for him, this should be enough."