Into Unscientific

"."

Although there are many emotions in my heart at this time, the emotions are extremely complicated.

But as a scientific researcher with an extremely rational personality, Xu Yun still has a part of clarity in his mind.

So he knows.

Now is not an occasion to give thanks or express emotion. Physics enthusiasts all over the world are paying attention to the situation here.

No matter how complicated the emotion is, we can only wait until the stage to talk about it.

Now his top priority is not to love his children, but to show his abilities as much as possible, so that Zhou Shaoping's good intentions cannot be wasted.

Think here.

Xu Yun couldn't help taking a deep breath, and cast a grateful look at Zhou Shaoping.

Immediately, the expression of the whole person returned to its original calm again.

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, then nodded:

"feasible."

Zhou Shaoping's words were not out of politeness, Xu Yun's train of thought really surprised him a little.

Actually.

When Xu Yun was first named as an assistant, Zhou Shaoping did have a little idea of ​​setting up a stage for Xu Yun, but this idea was not strong at first.

After all, the premise of setting up the stage is that Xu Yun has real talent and learning, or in other words, he has shown real talent and learning on a certain issue.

Otherwise, wouldn't it be the same as wanting to boast about acting skills without acting skills, or even fake attendance to swipe tickets?

If so.

Xu Yun, Zhou Shaoping and even the entire Chinese scientific community will be reduced to a laughing stock.

It is true that Zhou Shaoping is willing to be Chunni, but it does not mean that he will do some stupid things.

So at the beginning, he just wanted to wait and see first, to see if there was any chance to set a stage for Xu Yun.

Later, the part that included the pseudo-scalar stuck was also a real situation he encountered, not a trick of pretending.

The result was unexpected.

Xu Yun's thinking was so quick that he gave a very subtle calculation direction within a few minutes.

In addition, Zhou Shaoping made such a temporary decision based on his previous cooperation experience in Jinping Deep Earth Laboratory.

That is to say, the 'cause' of Xu Yun's genuine ability is the 'result' of Zhou Shaoping's choice.

Therefore, Zhou Shaoping really agrees with Xu Yun's thinking.

After Zhou Shaoping made a 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.

Like the Fermi surface, the rotation matrix is ​​also a thing covering many fields.

For example, the shader also has a rotation matrix in the programming field, but the rotation matrix of the shader is very easy.

Just do sine-cosine expansion through the sine-cosine relationship, then make it into a matrix multiplication format, and then use three vector point multiplications as the orthogonal basis.

But in the field of particle physics?

This matter is more complicated.

Because it involves the canonical quantization category of the real scalar field.

well known.

For a classical mechanical system composed of n mass points, 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.

And for the field Ψ, its Lagrangian density function L can be defined as:

L=L(Ψ, μΨ) is marked as 2.

And the Lagrangian 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 matter field (except the gravitational field) should be written as:

L=L(Ψ, μΨ) is marked as 3.

For microscopic systems, it is generally not necessary to consider gravity, so we only care about Equation 2.

The Lagrangian function obtained from Equation 2 is:

L=∫L(Ψ,μΨ)d3x

=∫L(Ψ,Ψ,1ctΨ)d3x

=∫L(Ψ,1cΨ˙)d3x marks it as 4.

That's right.

See here.

Presumably many students have already understood it.

The meaning of this formula is very clear:

It can be understood as dividing the space into small boxes with a volume of dv, in which the average value of the field of the small box numbered i is Ψi, and let qi=Ψidv,

Then (4) can be written in the form of (1):

L=L(qi,q˙i).

In this way.

The physical meaning of the field quantity Ψ is equivalent to the generalized coordinates in formula (1), that is, a system can only be formally carried out after a system has been constructed.

Still very simple and easy to understand.

Swish Swish Swish——

This time, Xu Yun did not rely on a computer for the derivation process, but performed calculations by hand.

After all, handwriting is easier to enter the state than the keyboard in many cases.

What's more, although Dirichlet's ranking in the history of mathematics is only in the early 20s, his calculation ability can enter the top ten:

In the original Night of Pluto, Dirichlet was responsible for the calculation of the deviation value of the Yinjing. (Why did some people say yesterday that Xu Yun has never seen Dirichlet? Stretch your head and I will give you a buff)

So here and now.

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"

"Consider the particle of 'Pluto' as a situation similar to a mass point, for the field, its operator has the following basic commutation relation, [π^(r, t), φ^(r', t)]=iδ3(rr ’) and [π^(r, t), π^(r′, t)]=[φ^(r, t), φ^(r′, t)]=0”

"So the Lagrangian density function of its free real scalar field φ is L=12ημνμφνφ12mcφ=12ctφ12(φ)12mc2φ."

The formula line by line was written down by Xu Yun.

Zhou Shaoping, who was opposite him, was not idle either, and took the initiative to work on the spin angular momentum operator and its commutation relationship and Pauli matrix.

"[s^i, s^j] = iij ks^k"

"Order {s^+=s^x+is^ys^=s^xis^y"

"Then: [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 contact between the fingertips and the calculation paper was unexpectedly pleasant at this time, as if playing a symphony with a special melody.

After the previous decision to calculate separately.

David Gross, Polyakov, Nima, Higgs, Te Hooft and others also convened assistants and helpers to form a calculation team.

Each team consists of at least two people, three more, and Higgs' team has four.

The calculation content of each team is consistent, that is, multiple teams jointly calculate, and finally compare the results, so as to avoid the influence of calculation due to errors.

At the same time, in order to facilitate the audience to watch, several major live broadcast platforms also thoughtfully provided the live broadcast angles of the corresponding groups.

This kind of thing is very common in 2023.

For example, games will have players’ perspectives, sports games will have multiple camera positions, etc.

In the basketball game on a certain news platform, there is even a drinking fountain perspective, which can be called murderous.

And in these perspectives.

As the computing team representing the host team, Zhou Shaoping and Xu Yun also received the highest attention.

At present, the popularity of Zhou Shaoping's group is much higher than that of Te Hooft and others, even the protagonist Wei Teng is not as popular, but it is a well-deserved popular perspective.

The high degree of attention, in turn, has prompted the cameraman to focus on Zhou Shaoping and Xu Yun.

For example right now.

The backstage of the live broadcast deliberately divided Xu Yun and the others into two groups of detailed shots.

One group is relatively normal, including the images of the area where Xu Yun and the two are sitting, which is the standard frontal image that everyone recognizes.

If I use a specific example to describe it, it is somewhat similar to the scene where the host organizes the speech when the host ends the broadcast in the news network.

The other group is quite special - it is a telephoto picture.

The camera is located above the heads of Xu Yun and Zhou Shaoping, and the screen captures the content of Xu Yun and Zhou Shaoping's calculation paper.

That is to say, through this lens, the audience can understand Xu Yun's calculation ideas and progress.

While Xu Yun and Zhou Shaoping were calculating the data.

In the major live broadcast rooms, there are also a large number of bullet screens floating by, and it looks very lively:

[Grass, I'm blind! 】

[Who can tell me this thing. Are physics people so scary? 】

[I feel that there seems to be a callus on the knuckle of Dr. Xu's right index finger. Could it be left by long-term dancing with a spear and stick?]

[There is a question, is the density function wrong? Why is tφ=c2π? 】

[The above is correct, here we need to use boundary conditions, Dr. Xu simplified it]

[Oatmeal Search Roasted Fish Restaurant No. 5 Branch]

[Cpdd! 】

All kinds of gossip, complaints, and barrage of academic exchanges filled the major live broadcast rooms.

At the same time, there are also various dynamics on the major social media.

More than 90% of the contents of these dynamics are complaining about not being able to understand the calculation process, like a bible.

There are also a small number of minkes who say that physics does not exist, and take the opportunity to promote that they have overturned the theory of relativity, hoping that someone can pay for printing works.

In addition, there are some people who, like the previous Liner Lab, are competing with Xu Yun and others with a sense of competitiveness.

For example, a blogger whose nickname is Dongfang Xile and whose certification information is "Researcher of High Energy Physics Research Group of National Science Base" soon posted a post:

[(Frightened emoticon package) I took a look at the live broadcast. Judging from the current progress, the derivation speed of the group of Academician Zhou and Dr. Xu seems to be a little faster than that of Gross.]

I don't know if some keywords are triggered.

This Weibo was quickly posted on the square's homepage and received a lot of exposure.

Less than two minutes.

The number of Weibo comments exceeded 100.

Among them, the nickname of the most popular comment is [Promised to be King], and the content is very simple:

【real or fake? 】.

There are only two replies below this comment, and the first place is mainly because of the early comments.

But the second hottest 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 that of Gross’s group, but the starting directions of the two groups are different. Although Academician Zhou and the others are temporarily leading, how to fit the condition of continuous single value and bounded is a big problem, at least for me Discussed with several brothers, no one can think of a suitable solution. 】

There are more replies in this building, and they are basically professionals or physics enthusiasts who pay attention to this matter.

In just a few minutes, everyone discussed more than 40 floors.

But including the blogger Dongfang Xile, the plans that everyone came up with were all rejected one after another.

Then another ten minutes passed.

Wink suddenly posted an independent update on his personal page:

[Fuck, I've learned a lot, can I still answer it from a specific wave number? 】

Wink is also a niche blogger, with a lot of fans on his account.

So soon, a fan left a message:

【W big, that means that Dr. Xu Yun is really powerful? 】

Ten seconds later.

Following the news, Dongfang Joy and Wink sent replies one after another:

【It's really powerful, much stronger than me】

【.Extremely strong, I don’t know how the brain grows, maybe there is a cheat to please God (laughs), in short, we can look forward to it in the future, this child is so terrifying! 】

This moment.

As the live broadcast continued, some similar comments appeared one after another in every corner of the Internet.

The more people in the industry, the more he understands the strength Xu Yun has shown this time—except for that kind of jealous sour.

all in all.

A subtle image of a schoolmaster slowly formed in some people's minds.

Even in individual dynamics.

Some people have already interpreted Xu Yun's fledgling status as a closed social circle caused by his dedication to academics, and praised that this is the spirit of scientific research.

In some more troublesome water blowing groups, there are even members of the sand sculpture group playing the dragon ball stalk of "Let's raise our hands and lend our strength to Xu Yun".

Of course.

This kind of meme will have a little more meaning, but at least it will be emotionally friendly.

This is the beauty of the Internet age.

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 remarks on the Internet.

Now he and Zhou Shaoping have been advancing smoothly for a period of time, and finally encountered the biggest challenge they have faced today.

well known.

Compared with classical mechanics, particle physics has one characteristic that is very obvious:

Particle physics transforms the mechanical quantity into an operator, and regards the mechanical quantity as an operator.

Therefore, after calculating the Lagrangian density.

Xu Yun and the others had to transform the canonical momentum density and field quantity into operators before proceeding to the next step.

"."

on the desk.

Looking at the counting 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 formula on the paper with a pen, paused the tip of the pen, turned around 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 pretending deliberately.

Actually.

At this point, there is no need for Zhou Shaoping to deliberately create opportunities for Xu Yun, one time is enough for similar things.

Then he looked at David Gross and Polyakov, the nibs of the two groups did not stop.

Xu Yun saw several plural C characters on their manuscript paper, which means that the entry point of the two big guys' team is the vector rotation model with limited angle.

See this situation.

A trace of hesitation flashed in Xu Yun's eyes.

In the previous calculation process, he actually considered this direction.

After all, in terms of difficulty, vector rotation with a limited angle is easier than designing a matrix element that rotates around the y-axis.

but

For some reason, Xu Yun always felt that there seemed to be some inexplicable problems in this direction.

In addition, at this time, he still has Dirichlet's mind card attached to him, and his field of vision is not as wide as that of Gaussian wheat, but at least higher than that of David Gross and others:

David Gross and Polyakov are ranked between 5-8 in current physics, and they belong to the existence above the Nobel Prize, but they are not particularly high in the entire history of physics.

If they hadn't had a dazzling breakthrough before their death, their ranking in the history of physics would probably be between 60-80, which is Landau's 1.5-2 gear.

Due to his own premonition and the field of vision given by Dirichlet, Xu Yun finally chose to give up the limited-angle vector rotation.

But the current operatorization has really stumped Xu Yun and Zhou Shaoping.

If this problem is not resolved, everything that follows will be empty talk.

Considering that language communication might give some black people the opportunity to hit the morale of the live broadcast, Xu Yun and Zhou Shaoping mainly communicated in written language in the following time.

Basically, one party writes down a few formulas, and the other party can quickly understand them.

"."

After more than ten minutes.

Xu Yun shook his head towards Zhou Shaoping again, and sighed secretly.

This is already the fifth time the two of them have rejected the plan together. Whether it is the method Xu Yun came up with or Zhou Shaoping's inspiration, the problem was quickly found out.

Think here.

Xu Yun's brows furrowed even more.

Mentioned earlier.

The 'Pluto' particle does not belong to known subatomic particles, so the operatorization process is not so much a 'calculation' as a 'customization'.

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 a little embarrassed at this time.

And just when Xu Yun and Zhou Shaoping felt 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."

Do not know why.

When he heard this voice, Xu Yun subconsciously thought of Mr. Wang in 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:

"Old Yang?! How did you get here?"

That's right.

The person standing behind Xu Yun who made the sound was obviously Mr. Yang who hadn't spoken much today!

At this time, Elder Yang's face was still a little sluggish, but perhaps because he had rested in his seat for a while, his spirit was much better than before.

Seeing Xu Yun looking at him in surprise, Mr. Yang smiled and stretched out his right palm and pressed it down:

"After a short rest, I feel better, Xiao Xu, go back to your seat first, and see if my plan can work. Our time is limited."

Hearing what Mr. Yang said, Xu Yun quickly recovered from his previous surprise.

He hastily pulled a chair from his side for Mr. Yang to sit down, and then he himself sat back down.

Although there are many things to say in my heart, it is obviously not a good time to chat.

There was a trace of hesitation in Elder Yang's tone, it could be seen that he was affected by his energy, and he was not so sure about his own thoughts.

Then Xu Yun took a deep breath, forced himself to calm down, and quickly calculated on the paper.

The eigenstate equation of the Hamiltonian operator calculated by Xu Yun before 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 an obvious abnormal interval φk and an i, and the two cannot be connected through transformation.

But if you think of it as a wave function

Mentioned earlier.

Wave functions are complex numbers, and complex numbers can have imaginary parts.

The reason why the probability equation of the particle orbit cannot use the imaginary part is that the mass may be negative, but the operatorization process does not need to take this into account.

seem

really doable?

Think here.

Xu Yun's speed of writing was 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 relativity, so ttφk=ωkφk."

"At the same time, for a free field, the energy density corresponding to the wave number k is uniform."

And the other side.

Zhou Shaoping is also doing the same calculation.

rustle——

Looking at Xu Yun and Zhou Shaoping who were calculating, Elder Yang also looked a little serious.

During the first hour of the calculation, Mr. Yang was recuperating in his seat, and he really didn't have the energy to pay attention to the whole process.

When he woke up, Xu Yun and Zhou Shaoping had already made a plan to rotate the matrix elements of the operator around the y-axis.

One of the bases of this scheme is Yang Lao's Yang Mills field, so when Xu Yun calculated the Hamiltonian eigenstate equation, Yang Lao realized that they might encounter problems.

Although I don't know why Xu Yun didn't choose the simpler vector rotation with a limited angle, but it's too late to turn around at this time, so Yang Lao cheered up and began to think about the solution by himself.

Relying on his own solid physical foundation, Mr. Yang really thought of a plan, but he was only 60% to 70% sure. For an elder who is over a hundred years old and has listened to the report for several hours, this is a plan. It is already an exaggerated value.

After more than ten minutes.

Xu Yun and Zhou Shaoping put down their pens at the same time.

Zhou Shaoping first looked at Mr. Yang, then asked Xu Yun:

"Xiao Xu, what's your result?"

Xu Yun moved the pen away and pushed the paper to Zhou Shaoping.

Zhou Shaoping took a few glances, and suddenly pushed his own calculation paper forward.

Swish——

The two pieces of calculation paper were butted together head-to-head.

And through the lens above, it can be seen that the same general solution is written on the two pieces of paper:

ψ(φk)=C1Dv1(iωkcφk)+CDv(2ωkcφk).