Chapter 453 Mr. Yang: It doesn’t matter, I will take action
"."
Although my heart was full of emotions at this time, the emotions were extremely complicated.
But as a scientific researcher with an extremely rational personality, Xu Yun still retains some clarity in his mind.
So he knew it.
Now is not the time for acknowledgments or expressions of emotion. Physics enthusiasts around the world are paying attention to what is going on here.
Even the most complicated emotions can only be expressed on stage.
His top priority now is not the love between his children, but to demonstrate his abilities as much as possible and not let Zhou Shaoping's good intentions go to waste.
Think of this.
Xu Yun couldn't help but take a deep breath and cast a grateful look at Zhou Shaoping.
Immediately, the whole person's expression returned to its original calmness.
As if nothing had happened, he looked like a student asking for advice, and asked Zhou Shaoping:
"Academician Zhou, do you think my plan is feasible?"
Zhou Shaoping thought for a moment and nodded:
"It works."
Zhou Shaoping's words were not polite. Xu Yun's idea really surprised and surprised him.
Actually.
When Xu Yun was first named as his assistant, Zhou Shaoping did have some idea of setting up a stage for Xu Yun, but this idea was not strong at first.
After all, the prerequisite for setting up the stage is that Xu Yun has real talent and learning, or that he has shown real talent and learning on a certain issue.
Otherwise, wouldn't it be the same as trying to boast about your acting skills without having any acting skills, or even making false attendance figures to boost tickets?
If that's the case.
Xu Yun, Zhou Shaoping and even the entire Chinese scientific community will become a laughing stock.
Zhou Shaoping is willing to make spring mud, but that doesn't mean he will do something stupid.
Therefore, at the beginning, he just wanted to wait and see if there was any opportunity to set up a stage for Xu Yun.
Later, the part that included the pseudo-scalar jam was a real situation he encountered, not a pretense.
The result was unexpected.
Xu Yun's thinking was so quick, and he came up with a very sophisticated calculation direction within a few minutes.
Coupled with the previous cooperation experience in Jinping Deep Laboratory, Zhou Shaoping made such a decision on the spur of the moment.
That is to say, the 'cause' of Xu Yun's genuine ability was the 'effect' of Zhou Shaoping's choice.
Therefore, Zhou Shaoping did agree with Xu Yun's ideas.
After Zhou Shaoping made his decision.
Xu Yun no longer hesitated and began to calculate the matrix elements of the rotation operator around the y-axis.
This is actually not an easy job.
The rotation matrix, like the Fermi surface, is also a tool covering many fields.
For example, shaders also have rotation matrices in the programming field, but the rotation matrix of shaders is very easy.
Just do the sine and cosine expansion through the sine and cosine relationship, then make it into a matrix multiplication format, and then use three vector dot products as the orthogonal basis.
But when it comes to the field of particle physics
This matter is more complicated.
Because it involves the regular quantization category of real scalar fields.
As everyone knows.
For a classic mechanical system composed of n particles, its generalized coordinates can be defined as qi (i=1, 2, ., N).
Where N=3n is the dimension of the generalized coordinate space.
At this time.
The Laplace function of the system is defined as:
L=L(qi, q˙i), this formula is marked as 1.
For the field Ψ, its Laplace density function L can be defined as:
L=L(Ψ,μΨ) is marked as 2.
And the Laplace density function L is a scalar, where the field Ψ can be a scalar, spinor, vector or tensor.
Therefore, in curved space-time, the Lagrangian density of the general material field (except the gravitational field) should be written as:
L=L(Ψ,μΨ) is marked as 3.
For microscopic systems, gravity generally does not need to be considered, so we only care about equation 2.
The Laplace function of the field obtained from Equation 2 is:
L=∫L(Ψ,μΨ)d3x
=∫L(Ψ,Ψ,1ctΨ)d3x
=∫L(Ψ, 1cΨ˙)d3x and label it 4.
That's right.
See here.
Many students must have understood this already.
The meaning of this formula is very clear:
It can be understood as dividing the space into small square boxes with a volume of dv, where the average value of the field of the small square box numbered i is Ψi, and let qi=Ψidv,
Then equation (4) can be written in the form of equation (1):
L=L(qi,q˙i).
This way.
The physical meaning of the field quantity Ψ is equivalent to the generalized coordinates in equation (1), that is, only after a system has been constructed can subsequent calculations be formally carried out.
Still very simple and easy to understand.
Swish Swish Swish——
This time Xu Yun's derivation process did not rely on a computer, but performed calculations by hand.
After all, handwriting is often easier to get into than the keyboard.
What's more, although Dirichlet ranks only in the early 20s in the history of mathematics, his calculation ability can enter the top ten:
In the original Pluto Night, Dirichlet was responsible for calculating the galactic deviation value. (Why did some people say yesterday that Xu Yun has never seen Dirichlet? Put your head over here and I will give you a buff)
So at this moment.
Xu Yun can be said to be a real "god" in writing.
"The canonical momentum corresponding to qi is pi=Lq˙i, so the canonical momentum density can be defined as π(r, t)=L(tΨ)"
"So the Hamiltonian of the system is H=∫(π(r,t)tΨL)d3x"
"Considering 'Pluto' particles as similar to particles, for fields, their operators have the following basic commutation relations, [π^(r, t), φ^(r′, t)]=iδ3(rr ′) and [π^(r, t), π^(r′, t)]=[φ^(r, t), φ^(r′, t)]=0”
"Therefore, the Laplace density function of its free real scalar field φ is L=12ημνμφνφ12mcφ=12ctφ12(φ)12mc2φ."
Lines of formulas were written down by Xu Yun.
Opposite him, Zhou Shaoping was not idle either, and took the initiative to work on the spin angular momentum operator, its commutation relationship, and the Pauli matrix.
"[s^i,s^j]=iijks^k"
"Let {s^+=s^x+is^ys^=s^xis^y"
"Then we get: [s^+, s^]=(s^x+is^y)(s^xis^y)(s^xis^y)(s^x+is^y)=i(s^ ys^xs^xs^y)+i(s^ys^xs^xs^y)=2i[s^y,s^x]=2i(is^z)=2s^z”
The sound of the fingertips touching the calculation paper was unexpectedly melodious at this moment, like a symphony playing a special melody.
After previously deciding to calculate separately.
David Gross, Polyakov, Nima, Higgs, Tehuft and others also recruited assistants and helpers to form a calculation team.
Each team consists of at least two people, and as many as three. Higgs's team has four people.
The calculation content of each team is consistent, that is, multiple teams perform calculations together, and finally compare the results to avoid errors affecting the calculation.
At the same time, in order to facilitate the viewing of the audience, several major live broadcast platforms also thoughtfully provided the live broadcast perspectives of the corresponding groups.
This kind of thing will be very common in 2023.
For example, games will have player perspectives, sports games will have multiple cameras, etc.
In a basketball game on a certain news platform, there is even a drinking fountain perspective, which can be described as murderous.
And in these major perspectives.
As the computing team representing the host, Zhou Shaoping and Xu Yun received the most attention.
At present, the popularity of Zhou Shaoping's group is much higher than that of Tehuft and others. Even the protagonist Witten is not as popular as him. It is a well-deserved popular perspective.
The high level of attention, in turn, prompted cameramen to focus on Zhou Shaoping and Xu Yun.
For example, right now.
The backstage of the live broadcast deliberately divided the scenes of Xu Yun and the others into two groups of detailed shots.
One group is relatively normal, covering the area where Xu Yun and the two are sitting, which is the standard frontal image that everyone knows.
To use a specific example to describe it, it is somewhat similar to the scene in the news broadcast where the host is sorting out the speech notes after finishing the broadcast.
The other group is more special - it is a telephoto picture.
The camera is located above the heads of Xu Yun and Zhou Shaoping, and the screen captures the contents of Xu Yun and Zhou Shaoping's calculation manuscript paper.
It is through this lens that the audience can understand Xu Yun's calculation ideas and progress.
While Xu Yun and Zhou Shaoping were calculating the data.
There are also a lot of barrages floating in the major live broadcast rooms, and it looks so lively:
[Oops, my eyes are blind! 】
[Who can tell me this thing? Is it so scary for all those who do physics? 】
[I feel like there is a callus on the knuckle of the index finger of Dr. Xu’s right hand. Could it be caused by long-term gun and stick dancing]
[I have a question, is the density function calculated wrong? Why is tφ=c2π? 】
[The previous one is correct, boundary conditions should be used here, Dr. Xu simplified it]
【Oatmeal Search Shaoyu Restaurant No. 5 Branch】
【Cpdd! 】
All kinds of chats, complaints and barrages of academic exchanges filled the major live broadcast rooms.
At the same time, various updates are constantly being posted on major social media.
More than 90% of the contents of these updates are complaints about not being able to understand the calculation process, which is like a bible.
There are also a small number of civil scientists who are saying that physics does not exist, taking the opportunity to promote that they have overturned the theory of relativity, and hope that someone can fund the printing of their works.
There are also some people who are competing with Xu Yun and others with a competitive spirit just like Liner Lab before.
For example, a blogger whose nickname is Dongfang Xile and whose certification information is ‘researcher of the High Energy Physics Research Group of the National Science Base’ quickly posted a message:
[(horror emoticon) I just took a look at the live broadcast. Judging from the current progress, the derivation speed of Academician Zhou and Dr. Xu’s group seems to be a little faster than Gross’s group]
I don’t know if certain keywords were triggered.
This Weibo post was quickly posted on the home page of the square and received a lot of exposure.
Less than two minutes.
The number of Weibo comments exceeded 100.
Among them, the most popular comment is nicknamed [Promise to Be King], and its content is very simple:
[Real or false? 】.
There are only two floors of replies under this comment. It ranks first mainly because I commented early.
But the second most popular floor is different.
The comment account on the second floor is also a big V. The certification label is a graduate student in the Department of Physics of Harbin Institute of Technology, and the nickname is wink:
[Academician Zhou’s progress is faster than Gross’s group, but the starting directions of the two groups are different. Although Academician Zhou and the others are temporarily ahead, how to meet the conditions of continuous and bounded single values is a big problem, at least for me After discussing it with several senior brothers, no one could think of a suitable solution. 】
There are many replies in this building, and they are basically professionals or physics enthusiasts who are concerned about this matter.
In just a few minutes, everyone discussed more than 40 floors.
However, the plans that everyone came up with, including blogger Dongfang Xile, were rejected one after another.
Then another ten minutes passed.
Wink suddenly posted an independent update on his personal page:
[Damn it, now that you have gained experience, can you still answer it from a specific wave number? 】
Wink is also a niche blogger with a lot of active fans on his account.
So soon, a fan left a message:
[Da W, does that mean that Dr. Xu Yun is indeed very powerful? 】
Ten seconds later.
Dongfang Xile and wink, who followed the news, sent replies one after another:
[It is indeed very powerful, much better than me]
[.Ultimately strong. I don’t know how my brain grows. Maybe there is a cheat to please God (laughs). Anyway, you can look forward to it in the future. This kid is so scary! 】
At this moment.
As the live broadcast continued, some similar comments began to appear in every corner of the Internet.
The more insiders are in the industry, the more they understand the strength Xu Yun has shown this time - except for the jealous and sour guy.
all in all.
A subtle image of a top student slowly formed in some people's minds.
Even within individual dynamics.
Some people have begun to interpret Xu Yun's status as a fledgling as a result of being immersed in academia, and praised him as the spirit of scientific research.
There are also some more trouble-making groups, and some members of the sand sculpture group even play the Dragon Ball meme of "Let's raise our hands high and lend our strength to Xu Yun."
Of course.
This kind of meme means a little more, but at least it is emotionally friendly.
This is the advantage of the Internet era.
After an image begins to be established, even if it is not so three-dimensional in the initial stage, it can become some foreshadowing in the future.
Of course.
At this time, Xu Yun did not understand these comments on the Internet.
Now, after making smooth progress for a while, he and Zhou Shaoping finally encountered the biggest challenge they had faced today.
As everyone knows.
Compared with classical mechanics, particle physics has one very obvious feature:
Particle physics transforms mechanical quantities into operators and treats mechanical quantities as operators.
So after calculating the Rascal density.
Xu Yun and the others must convert the canonical momentum density and field quantities into operators respectively before they can proceed to the next step.
"."
On the desk.
Looking at the calculation paper in front of him, Zhou Shaoping was silent for a moment and said to Xu Yun:
"Xiao Xu, do you have any ideas?"
Xu Yun quickly wrote half a line of formulas on the paper. He paused with the pen tip, turned back and drew a line along the waist of the formula, and shook his head at the same time:
".Not yet, what about you?"
Zhou Shaoping also shook his head.
Seeing this, Xu Yun looked at Zhou Shaoping calmly.
I found that the well-known academician's expression was very serious at this time, and he didn't seem to be deliberately pretending.
Actually.
At this point, there is no need for Zhou Shaoping to deliberately create opportunities for Xu Yun. A similar incident is enough once.
Then he looked at David Gross and Polyakov. Their pen tips did not stop.
Xu Yun saw several plural C characters on their manuscript paper, which meant that the entry point of these two big team teams was the limited-angle vector rotation model.
See this situation.
A trace of hesitation flashed in Xu Yun's eyes.
In the previous calculation process, he had actually considered this direction.
After all, in terms of difficulty, vector rotation with a limited angle is easier than designing a matrix element with a rotation operator around the y-axis.
But
For some reason, Xu Yun always felt that there seemed to be some unexplainable problems in this direction.
In addition, he is still possessed by Dirichlet's thinking card at this time, and his field of vision is not only comparable to Gaussian Wheat, but at least higher than David Gross and others:
The rankings of David Gross and Polyakov in modern physics are probably between 5 and 8, which are above the Nobel Prize, but they are not particularly high in the entire history of physics.
If they did not make too dazzling breakthroughs before their death, their ranking in the history of physics would probably be between 60 and 80, which is Landau's 1.5-2 level.
Xu Yun finally chose to give up vector rotation at a limited angle due to his own premonition and the vision given by Dirichlet.
But the current operatorization really stumps Xu Yun and Zhou Shaoping.
If this problem is not solved, everything that follows will be empty talk.
Considering that language communication may give some little black men the opportunity to undermine the morale of the live broadcast, Xu Yun and Zhou Shaoping mainly relied on written language to communicate in the following time.
Basically, if one party writes down a few formulas, the other party can quickly understand them.
"."
More than ten minutes later.
Xu Yun shook his head at Zhou Shaoping again and sighed secretly.
This was the fifth time that the two of them had rejected the plan. Whether it was Xu Yun's method or Zhou Shaoping's inspiration, the problem was quickly discovered.
Think of this.
Xu Yun's brows furrowed even more.
Mentioned before.
The 'Pluto' particle is not a known subatomic particle, so the process of calculating its operator is more of a 'customization' than a 'calculation'.
That is to say, many steps cannot refer to known models, and the difficulty is much more difficult than the operatorization of ordinary particles.
Even with the blessing of Dirichlet's vision, Xu Yun was still in a bit of trouble at this time.
Just when Xu Yun and Zhou Shaoping were feeling a little anxious.
A weak voice suddenly sounded from behind Xu Yun:
"Xiao Xu, try to make a specific wave number K, treat the field quantity as a wave function instead of a coordinate operator, and try to calculate its general solution."
Don't know why.
When he heard this sound, Xu Yun subconsciously thought of Mr. Wang from Jinping Laboratory at that time.
Then he turned his head curiously, wanting to see who the other party was.
As a result, after seeing this person's face clearly, Xu Yun stood up from his seat with a "whoosh" and said in surprise:
"Mr. Yang?! Why are you here?"
That's right.
The person standing behind Xu Yun who spoke out was Mr. Yang who had not spoken much today!
At this time, Mr. Yang's face was still a little sluggish, but perhaps because he rested in his seat for a while, his energy level was much better than before.
Seeing Xu Yun looking at him in surprise, Mr. Yang smiled and stretched out his right hand and pressed it down:
"After resting for a while, I feel better. Xiao Xu, please go back to your seat first and see if my plan can be used. We have limited time."
After hearing what Mr. Yang said, Xu Yun quickly recovered from his previous surprise.
He quickly pulled a chair from beside him for Mr. Yang to sit down, and then sat back down himself.
Although there is a lot to say in my heart, it is obviously not a good time to chat now.
There was a hint of hesitation in Mr. Yang's tone, and it could be seen that he was not so sure about his idea due to his energy.
Then Xu Yun took a deep breath, forced himself to calm down, and quickly calculated on paper.
The eigenstate equation of the Hamiltonian operator previously calculated by Xu Yun is as follows:
H^=∑k(c/2(iφk)+ωkcφk/2)
It can be clearly seen here that the identity of the field quantity φk is a generalized coordinate operator.
This operator and the subsequent spin variable σ have obvious abnormal intervals φk and an i, and the two cannot be connected through transformation.
But if you think of it as a wave function
Mentioned before.
The wave function is a complex number, and complex numbers can have imaginary parts.
The reason why the probability equation of particle orbit cannot use the imaginary part is because the mass may be negative, but the operatorization process does not need to take this into account.
It seems
Is it really possible?
Think of this.
Xu Yun's writing speed suddenly became much faster.
“H=∫(c/2π(r,t)12cφttφ)d3r”
"ttφ=Ekφ,Ek=kc+mc^4"
"The wave number k is the reciprocal of the wavelength, that is, k=2πλ, which satisfies the energy relationship of the theory of relativity, so ttφk=ωkφk."
"At the same time, for the free field, the energy density corresponding to the wave number k is uniform."
And the other side.
Zhou Shaoping is doing the same calculation.
Shashasha——
Looking at Xu Yun and Zhou Shaoping who were calculating, Mr. Yang's expression also looked a little serious.
In the first hour of calculation, Mr. Yang had been practicing in his seat and really had no energy to pay attention to the whole process.
When he woke up, Xu Yun and Zhou Shaoping had already decided on the plan for the matrix element of the rotation operator around the y-axis.
One of the foundations of this plan is Lao Yang's Yang Mills field, so Lao Yang realized that they might encounter problems when Xu Yun calculated the Hamiltonian eigenstate equation.
Although I don't know why Xu Yun didn't choose a simpler vector rotation with a limited angle, it was too late to turn around at this time, so Yang Lao steeled himself and began to think about a solution.
Relying on his solid foundation in physics, Mr. Yang really thought of a plan, but he was only 60 to 70 percent sure of it. For an elder who is over a hundred years old and has listened to several hours of lectures, this is not a solution. This is already a very exaggerated value.
More than ten minutes passed.
Xu Yun and Zhou Shaoping put down their pens at the same time.
Zhou Shaoping first looked at Mr. Yang, and then asked Xu Yun:
"Xiao Xu, what's the result of you?"
Xu Yun moved the pen away and pushed the calculation paper in front of Zhou Shaoping.
Zhou Shaoping glanced at it for a few times and suddenly pushed his calculation paper forward.
Swish——
The two calculation papers were butted together head to head.
As you can see through the lens above, the same general explanation is written on both pieces of paper:
ψ(φk)=C1Dv1(iωkcφk)+CDv(2ωkcφk). (End of chapter)