Into Unscientific

on the math table.

Looking at the two general solutions with exactly the same content in front of you.

While rejoicing at the breakthrough of a difficult problem, Xu Yun also felt a little emotion in his heart again.

He thought about what happened in Jinping's deep underground laboratory more than a week ago.

At that time, the re-inspection team composed of many academicians also encountered a very serious problem, which was stuck in the accuracy of the energy level of the W-boson.

As a result, everyone was thinking hard and to no avail.

Wang Lao, who was over a hundred years old, stood up.

He proposed a plan to optimize with J particles, and successfully solved this problem, which led to a series of subsequent events.

today.

How similar is Yang Lao's appearance this time to Wang Lao?

The same age is over 100 years old, the same state is not good, and the same blow goes straight to the key point

"An old man in a family is like a treasure"

Xu Yun sighed deeply, turned his head and looked at Zhou Shaoping who was opposite him.

Both of them saw a thought in each other's eyes:

You must not waste all of Yang Lao's hard work!

Say something that may not sound good but is true.

For an elder of Mr. Yang's age, this kind of plan that accurately covers the specific process will consume his lifespan!

Think here.

Xu Yun picked up the pen again and quickly proceeded to the next calculation.

Right now, following Mr. Yang's suggestion, the first step taken by Xu Yun and Zhou Shaoping is only a matter of calculation.

After all, Mr. Yang gave a general solution.

It is not difficult to understand its use by looking at the literal meaning of Tongjie.

So soon.

According to the energy operator E^=itφ and the free field as the eigenfunction of energy, Xu Yun obtained a brand new 'state'.

This 'state' refers to the ground state of the system before the vacuum state when the 'Pluto' particle does exist.

This involves particle physics. Or a very important model in quantum mechanics.

That is, energy is quantized, and there is an operator in this model called nk.

It means that the model has nk particles with wavenumber k—yes, nk k, not n k.

It is not difficult to see based on the general solution that Xu Yun and the others came up with.

When nk=0.

There is no particle in the system, but its energy is not 0, and its wave function is not 0 either.

This is a vacuum system, so the energy of "vacuum" is not zero.

That's right.

This is the prototype of the theory of the famous vacuum zero-point energy. However, concepts such as virtual particles need to be supplemented, which has nothing to do with the current situation, so I will not mention it for the time being.

all in all.

The state obtained by Xu Yun is the state before a system with 'Pluto' particles is transformed into a vacuum.

The general solution operator of this state, called the possession operator, has a normalization factor.

This normalization factor is a core data that Xu Yun and Zhou Shaoping are looking for this time.

Using a less rigorous but easy to understand example to describe is

We want to describe and locate a point on the plane. The simplest and most appropriate way is to express its position with the XY axis.

That is (4, 2) or (8, 3) and so on.

The normalization factor is equivalent to the X-axis coordinate.

After locking the normalization factor, the remaining link is naturally to find the Y-axis coordinates.

Once the two "coordinates" are all found, then the final goal can be locked.

Of course.

The actual normalization factor is a description of a probability distribution, which involves combinatorics, so I won’t go into details here.

"X-axis coordinates"

In the live media area, Chen Shanshan repeated the word, and asked Zhang Han curiously:

"Dr. Zhang, if the possession number operator is regarded as the X-axis coordinate, then what is the Y-axis coordinate that is needed?"

Zhang Han thought for a while and explained:

"The state calculated by Dr. Xu and Academician Zhou is located in a specific configuration space. For related content, please refer to Chapter 8.8.2 of Mr. Zeng Jinyan's "Tutorial of Quantum Mechanics", the second edition, specifically on page 151."

"So in addition to the possession operator, they had to compute a modulus square operator with an even number of permutations."

Chen Shanshan blinked:

"The modulus square operator?"

Zhang Han nodded affirmatively:

"Yes."

at the same time.

Lu Chaoyang, who had been watching Xu Yun's progress from the audience, also wrote down the words "modulus square operator" on the paper and drew a circle.

That's right.

After calculating the possession operator.

The next step for Xu Yun and Zhou Shaoping is to calculate the modulus square operator of the 'Pluto' particle.

Or to be more precise.

Angular Momentum.

Students who were particles in their previous life should know.

To talk about the properties of a certain particle is to talk about the characteristics of the Lagrangian of the field of this particle.

In this way.

The particle properties can be divided into two types:

The characteristics that can be reflected by the Lagrangian quantity, and the particle characteristics that are reflected by the interaction.

Among them, there are many particle properties that can only be reflected through interactions, such as the most representative concept of charge.

The so-called charge is actually the Noether charge derived from the U(1) symmetry of the compound field.

When considering the localization of U(1) symmetry, it is necessary to introduce some massless vector field to interact with this complex field.

If this massless vector field is an electromagnetic field, then the above-mentioned Noether charge is interpreted as an electric charge.

As for the properties of the free particles that can be directly reflected by the Lagrangian, there are only two kinds in total.

One is the mass of the particle, which is given by the coefficient of the Φ term in the Lagrange scale.

The second is the spin of the particle, which can be given by the Noether flow of the Lagrange quantity under the spatial rotation transformation.

For the 'Pluto' particles.

At present, including Xu Yun and Wei Teng, no one can calculate the mass of its particles because of insufficient information.

But spin is different.

There is a bad saying in particle physics that spin is an intrinsic property of particles.

What does intrinsic mean?

When the police interrogate a person in a TV series, everyone should have heard this sentence more or less:

"xxx, your disposition is actually not bad, it's just that you lack the correct guidance. After you go in, you should reform yourself and try to become a good person."

The disposition in this sentence is actually the same as the intrinsic nature of particles to some extent. It belongs to the "innate" attribute, and it will not be transferred by the environment at the beginning of its birth.

For example, a pigeon who writes a novel, although he owes dozens or hundreds of chapters to update, his own temperament is actually not bad, he is just a little lazy.

Of course.

This is just a metaphor.

In fact, the intrinsic properties of particles are very complex, involving gauge symmetry.

For example, the chubby Nima next to Xu Yun—here I will explain again, her name is really Nima, and her English name is Nima Arkani-Hamed.

A few years ago, Nima once said a famous saying:

3 is not equal to 2, which is gauge symmetry, and 2 is not greater than 3, which is intrinsic.

all in all.

Just like a two-dimensional surface such as a sphere does not depend on being embedded in a three-dimensional space, so curvature is its intrinsic property, and the modulus square operator is also an intrinsic property that can be calculated mathematically.

As long as the modulus square operator is determined, plus the previous occupancy number operator, the probability position of the ‘Pluto’ particle can be locked.

Or to be more precise.

This is a probabilistic position in mathematics, and whether it can be captured or not requires practical operation.

If Jade Emperor is not prepared to give face to the God of the West in his own territory, Wei Teng may end up fetching water from a bamboo basket in vain.

"Xiao Xu."

After confirming that he was ready to calculate the modulus square operator, Zhou Shaoping pondered for a moment and said to Xu Yun:

"In this way, the derivative of the spherical coordinate base vector with respect to each coordinate variable is left to you, no problem?"

Xu Yun flipped through the file and nodded quickly:

"no problem."

After he finished speaking, he paused, hesitated for a moment, and added:

"Academician Zhou, why don't you leave the radial and angular decomposition to me?"

What Xu Yun said was not to be brave, nor was it to grab the show, but to worry about Zhou Shaoping's body.

Although Zhou Shaoping is a round younger than Yang Lao, he is also approaching 90 years old. He has been busy for so long today, and his physical strength and energy are actually exhausted.

He, a 25-year-old young man, was a little tired at this time, and Zhou Shaoping's condition must be worse, but he just kept holding on.

In fact, it's not just Zhou Shaoping.

Except for the 50-year-old "young man" Nima, the rest of Higgs, Tehooft, and Polyakov are all 80-90 years old, and their energy consumption is not low at this time .

It’s just that the current situation is called group calculation, but it can also be regarded as a silent battlefield in essence. Everyone represents their own country—for example, Higgs is surrounded by British people, and the two assistants of Te Hooft They are also from the Netherlands, and Polyakov's assistant is a bear.

Therefore, although everyone was tired, no one was willing to leave first.

Zhou Shaoping obviously understood this too. He thought for a while, then nodded quickly:

"Okay, thank you for your hard work, Xiao Xu."

I heard this.

Elder Yang, who was opposite Zhou Shaoping, couldn't help but raised his head and glanced at him lightly.

Although Mr. Yang spent the first half of his life abroad all year round, he only returned to China at the end of 2003, and he did not have much entanglement or contact with domestic scientific research factions.

But Zhou Shaoping is also well-known internationally, so Yang Lao has heard of his character and experience.

In the early years, Zhou Shaoping had a student he liked very much, who was extremely talented. In his sophomore year, he was accepted as a disciple by Zhou Shaoping, who had already been elected as an academician.

A few years later, that student was admitted to graduate school and successfully entered Zhou Shaoping's project team.

results in an experiment.

Because Zhou Shaoping had been working overtime and was in poor health, the student offered to share part of the project for Zhou Shaoping, and Zhou Shaoping naturally agreed.

result

The student made a calculation error in a certain link, which caused the light source to overflow due to the excessive magnitude, causing serious damage to the equipment.

In the end, the whole project fell short, and the funding of more than 5,000 yuan was in vain.

To know.

That was five thousand dollars in 1983.

At the same time, because the experiment used a first-generation radiation source, the radiation rays beyond the limit directly passed through the longitudinal gradient dipole magnets, which caused the four recent researchers to be irradiated and suffered severe thermal radiation burns.

One of them died three years later, one had extremely serious sequelae of the lungs, and one was blind.

That's right.

This was the accident that happened at the Huairou base, and it was also a very serious experimental accident in the history of China's high-energy physics.

And the staff member who was blind was Zhou Shaoping's student Huang Wuxiang.

since then.

Although Zhou Shaoping is usually cheerful and doesn’t lose his temper, he has a very strange insistence on research:

He will never entrust others to do any tasks that have been set.

Zhou Shaoping has maintained this habit for 40 years, but he did not expect that today he would actually do it.

Make an exception?

Is it because of lack of energy?

Elder Yang glanced at Zhou Shaoping and shook his head slightly in his heart.

Not quite.

Although Zhou Shaoping did look a little tired, neither his complexion nor his calculation efficiency were far from the level of 'unable to sustain it'.

And since it is not due to physical strength, then there is only one answer——

Zhou Shaoping met a junior he could truly trust, and his confidence was so strong that it forcibly overwhelmed the nightmare in his heart.

Think here.

Elder Yang quietly glanced at Xu Yun beside him again, with a subtle expression on his face.

Zhou Shaoping, Zhang Gongding, Hou Xingyuan, Wang Lao. Oh, and Yang Lao himself.

Unconsciously.

This young man has had contact with so many academicians of the older generation, and has received their recognition and help, and has been given high hopes by one old academician after another.

Looking at the young generation in the entire Chinese scientific community, Xu Yun is the only one.

But it's very interesting.

He himself doesn't seem to realize this?

In fact, if Xu Yun can catch up to this chapter, he may be able to understand what Yang Lao is thinking through the content of the text.

But unfortunately, he does not have this ability.

So at this time, he didn't think about expectations or trust at all, but focused on the calculation of data.

After all, this is the final boss.

With the blessing of Dirichlet, Xu Yun's mind became clear.

Swish Swish Swish——

With the movement of the pen tip, a large number of formulas appeared on the calculation paper one by one.

The modulus square operator contains both the position operator and the momentum operator, and there is a very precise commutation relationship between them.

If it is a particle measured by a phenomenon, it is actually very easy to deduce it, just set a template.

But the problem is that the 'Pluto' particles have not been captured, so the derivation process is very troublesome.

And Xu Yun's entry point for this preparation is

Poincaré group.

Because the Poincaré group has a very special place:

Its representation can be completely determined by its obsessive subgroups and induced representations.

With the help of the representation of the small group of the universal cover of the Poincare group on the spin space, the irreducible unitary representation of the universal cover on the Hilbert space can be obtained, that is, the induced representation.

Different directional subgroups give different induced representations, corresponding to different single-particle states.

That is to say, the irreducible unitary representation of particles is completely determined by the basic symmetry of space-time, and there will be no interference from other factors.

Well, the above passage is standard Chinese characters and human words.

After a while.

Xu Yun wrote down the eigenstate of the operator l^z with an eigenvalue of m under the calculation content of the secret level:

l^+ψm=Cψm+1

At the same time [l^z, l^+]=l^+ can get l^zl^+=l^++l^+l^z=l^+(1+l^z), so it can be seen that l^+ is quite For a generation operator, l^ is equivalent to an annihilation operator.

They make the eigenvalues ​​of l^z always increase or decrease by an integer 1 in turn. When the square of the modulus of angular momentum is fixed and the maximum eigenvalue of l^z is m=l-1, then there must be l^+ ψl=0.

See here.

Maybe some of you Zhou Zhou students feel a little strange:

Why is the largest eigenvalue m=l-1, shouldn't it be equal to l?

the reason is simple.

Because when the square of the modulus of angular momentum is fixed and l is the maximum allowable value of m, the state with eigenvalue l+1 does not exist.

Since the system can always be in a state where the orbital angular momentum is 0, 0 must be an eigenvalue of the component operator l^z.

From the behavior of l^+ and l^, we can see that for the angular momentum component operator l^z, the difference between its adjacent eigenvalues ​​is always an integer 1.

Therefore, the eigenvalues ​​of the component operator l^z can only be m=0, ±1, ±2, .±l-1.

Of course.

Xu Yun was able to think of this, largely due to the vision he had at this time.

Just like Witten and the others ignored the distortion of the lone base vector before, the state of l+1 is not within the scope of conventional verification, and there are many more important processes than it.

And once the calculation is wrong here

So this derivation, at least the derivation of the Academy of Sciences team represented by Zhou Shaoping and Xu Yun, will completely fall short.

With that out of the way, all that's left is binary spinors.

During this process.

The eigenvalue σ of s^z needs to be regarded as a variable, and the spin wave function of the particle is a function of σ—as mentioned earlier, the spin of Pluto particles is a semi-odd number, that is, 1/2, 3 /2 or 5/2 etc.

Therefore, its matrix factor has only one form:

ξ′1η′2ξ′2η′1=(αδβγ)(ξ1η2ξ2η1).

This is a combination of two binary spinors, a scalar in the space of binary spinors.

write here.

Xu Yun flipped through the previous data again.

"Sure enough. The determinant is equal to 1, which is the real reason why the value of flux is too large."

In fact, in the previous process, Xu Yun always felt that there was a doubt that had not been answered:

That is, in the calculation of isolated particles, the expected background is 3.2fb^-1 - this is the data he personally detected, and he has detected it more than once.

But the corresponding flux value still becomes larger. Although the phenomenon seems to be due to the influence of the 'Pluto' particles, there is no suitable explanation for the spatial operator.

now it seems

The reason is because the transformed determinant is equal to 1.

That is, its external constraints have changed.

Because for non-relativistic situations, the physical meaning of ξ1ξ1+ξ2ξ2 is the probability of finding a particle at a certain point in space.

Therefore ξ1ξ1+ξ2ξ2 must be a scalar, that is, there should be:

ξ′1ξ′1+ξ′2ξ′2=(Uκ1ξκ)(Uκ1ξκ)+(Uκ2ξκ)(Uκ2ξκ)=ξ1ξ1+ξ2ξ2.

But for the case of relativity, the physical meaning of ξ1ξ1+ξ2ξ2 is no longer the probability of finding a particle at a certain point in space, but the time component of a four-dimensional vector.

That is, it has only 3 independent real parameters, and one of them is fixed. Wait!

Suddenly.

Xu Yun paused abruptly as he moved his pen on the paper, and a somewhat horrifying thought popped into his mind.

"Fuck, it can't be that thing, right?"