Looking at Xu Yun who confidently said the word 'on purpose'.
A big question mark suddenly appeared on Suzuki Atsushi's face.
Is this unlucky kid not acting according to common sense?
But soon.
Suzuki Atsushi recovered from his surprise, laughed angrily, and stared at Xu Yun:
"on purpose?"
"Xu Sang, that means you don't have to use the complete spectrum, and you deliberately do eigensquare root of the operator?"
Xu Yun nodded:
"That's right."
Suzuki Atsushi rolled his eyes silently. He originally thought that Neon Man's remarks when he discharged nuclear wastewater were shameless enough, but he didn't expect to meet someone with a thicker skin today:
"Why? Just because you want to show off your skills?"
Hear this.
Zhou Shaoping's expression on the other side of Suzuki Atsushi suddenly changed, and he subconsciously prepared to interrupt.
After all, if Xu Yun is allowed to continue talking, he won't be able to protect him even if he wants to when the responsibility is finalized.
This old guy, Atsushi Suzuki, has really sinister intentions...
However, before he could say anything, Zhou Shaoping felt someone tugging at his clothes.
He turned his head and found that Mr. Yang had arrived at a blind spot next to him at some point.
After meeting Zhou Shaoping's gaze, Mr. Yang glanced at him in a low voice:
"Xiao Zhou, let Xiao Xu continue."
Zhou Shaoping frowned when he heard this, and a trace of anxiety appeared on his face:
"But Mr. Yang, Xiao Xu will have no room for explanation at all..."
Before Zhou Shaoping finished speaking, he saw Mr. Yang waving his hand towards him again, interrupting the second half of his words.
After a while.
Perhaps because he was worried about the confusion of Zhou Shaoping's authorities, Mr. Yang hesitated for a moment and added faintly:
"Xiao Zhou, how do you know..."
"The data calculated by Xiao Xu must be wrong?"
Zhou Shaoping was stunned for a moment, and subconsciously wanted to retort, isn't this an obvious thing?
After all, the leaders of the other eight groups are either Nobel laureates or uncrowned kings like Witten, and there are also ultimate figures like Higgs.
Even the most popular person is a quasi-Nobel Prize winner like Atsushi Suzuki.
In the end, you said that Xu Yun’s answer was correct, but the other eight teams were wrong?
How is this possible?
But after the emergence of perceptual thinking, what follows is the rational thinking of a scientific researcher.
True.
Judging from the current magnitude of the relationship between the enemy and ourselves, the Academy group is undoubtedly an absolute minority.
But if analyzed theoretically...
Suddenly.
Zhou Shaoping's eyes became a little misty.
He thought of a possibility, the only possibility that fit the current situation.
But the probability of that happening is really too low...
And Zhou Shaoping's thinking also happened to eliminate the possibility of stopping Xu Yun.
Xu Yun pondered for a moment and shook his head at Suzuki Atsushi:
"Show off my skills? Mr. Suzuki, you misunderstood. How could I show off my skills on such an occasion?"
"It's just that during the previous calculation process, I discovered a somewhat serious problem."
"It was prompted by this problem that I chose another idea."
"what is the problem?"
"The pseudo-displacement value of finite-angle displacement rotation within a certain range does not comply with the law of superposition exchange."
"Pfft——"
Hearing Xu Yun's explanation, Suzuki Atsushi finally couldn't help laughing, as happy as Kennedy sitting in a convertible:
"Xu Sang, do you know what you are talking about? It does not comply with the law of superposition commutation?"
"The accuracy of finite-angle displacement rotation in terms of displacement connection has been tested for decades. Any current particle...even the Pangea dark matter discovered by the Chinese Academy of Sciences conformed to the corresponding model in the experiment just now.
"
"I don't deny that in some situations, the matrix elements of the rotation operator about the limited axis will indeed be more refined."
"But this kind of refinement is meaningless, not to mention that there are still many unresolved links in it. It is a real way to cause problems."
Hear this.
Many scholars around him nodded.
As Atsushi Suzuki said.
In current research in the physics community, finite-angle displacement rotation is a common method of constructing bases, and the fit covers all known particles.
It's simple and reliable, and has never gone wrong.
The matrix element of the rotation operator around the limited axis is indeed higher in accuracy, but this so-called accuracy does not mean much.
more importantly.
The perturbative basis constructed by matrix elements of the rotation operator around a limited axis is currently far from being thoroughly studied in the physics community.
[A novel app that has been running stably for many years, comparable to the old version of the source-changing app, huanyuanapp, that is used by all chasing bugs.]
Because the concept of total angular momentum is too broad.
Friends who have studied mechanics all know this.
Angular momentum is one of the three conserved quantities in classical mechanics.
But if you ask again why angular momentum is conserved, I guess fewer people will know.
Actually.
The reason why angular momentum is conserved is simple:
The rotational symmetry of space is the real cause of the conservation of angular momentum, that is, each continuous symmetry corresponds to a conserved quantity.
So more strictly speaking.
is to define the conserved quantity corresponding to the rotational symmetry of space as angular momentum.
In other words.
As a trace differential operator of a space rotation group, angular momentum can generate all space rotation transformations.
So different fields correspond to different angular momentum operators.
Take the spinor field as an example.
By calculating the spinor field, we can find that its angular momentum can be written in the form of J=L σ/2.
Where L is the orbital angular momentum, and σ/2 is called the spin of the particle corresponding to the spinor field.
In the particle stationary system, calculating the eigenvalue of the J operator shows that the eigenvalue is ±1/2.
This means that the spin of the particle corresponding to the spinor field is 1/2.
Since the spinor field must adopt the anti-commutative relationship when quantizing it, the spin 1/2 particles corresponding to the spinor field satisfy Fermi-Dirac statistics, so those particles are also called fermions - yes
, which is why the fermion spin is half-odd.
This chapter is not over, please click on the next page to continue reading! Among the 61 kinds of elementary particles, 36 kinds of quarks and 12 kinds of leptons (including electrons and neutrinos) are such fermions, 36 12 = 48 kinds.
Same reason.
The angular momentum of the loss field is also calculated, which also includes the spin term, and the particles with spin 1 corresponding to the loss field can be obtained.
Among the 61 kinds of elementary particles, 12 kinds of particles that transmit interactions are such spin 1 particles.
Including photons that transmit electromagnetic interactions, eight types of gluons that transmit strong interactions, and two W particles and one Z particle that transmit weak interactions. 1 8 3 = 12.
Calculation of the scalar field will reveal that it has no spin and corresponds to a spin-0 particle. The Higgs particle, the last particle discovered among the 61 fundamental particles, is such a particle.
look.
Currently, all basic particles have a direct mathematical relationship with the angular momentum operator.
In the words of Secondary School No. 1.
The matrix element of the rotation operator around the limited axis is the 'mystery' that touches the 'origin of the world'.
For example, Mr. Yang mentioned previously the idea of treating the field quantity as a wave function rather than a coordinate operator.
Don't just say a word about this idea.
In fact, after it is completely summarized as a mechanism, it is at least a paper at the level of the main journal of "Sce".
Give another example.
There is a limit to the amount of water a person can drink in one breath. Even if he is extremely thirsty, two bottles of 500 ml mineral water are almost enough.
Limited angle displacement rotation is equivalent to such mineral water.
The matrix element of the rotation operator around the limited axis is a 10-liter bucket.
The capacity of a 10-liter bucket is obviously larger than that of a mineral water bottle, but for a single person's drinking volume, the large capacity of the bucket is actually meaningless.
On the contrary, because of its large volume and heavy weight, carrying a bucket consumes more energy than mineral water.
Therefore, compared with the finite-angle rotation, the matrix element of the rotation operator around the limited axis is extremely cost-effective.
Then Suzuki Atsushi took a deep breath, suppressed the ecstasy in his heart, and pretended to be inquiring and curious:
"Oh? The pseudoquantity value in a certain range does not comply with the law of superposition commutation?"
"In that case... Xu Sang, can you find out the scope of the problem?"
Suzuki Atsushi's purpose was just to push Xu Yun to a point of no return. Unexpectedly, Xu Yun actually nodded happily:
"No problem. When TK is greater than 6, the constraint is greater than 7Φ, and the completely antisymmetric tensor is non-zero, what you get will be a mass loss field with a spin of 1/2 instead of 1, and the Lagrangian is at
There will be an extra negative sign in the form."
Suzuki Atsushi was stunned for a moment, and had a subconscious reaction in his mind:
Is this guy bluffing?
With such intensive calculations, can he still find the specific interval?
How can this be?
Anton Salinger, who was next to Suzuki Atsushi, reacted faster. He stepped over to the data terminal and compared the data seriously.
"TK is greater than 6...the constraint is greater than 7K-G field....the total antisymmetric tensor is non-0...."
Anton Salinger entered the data quickly, and after a few seconds, he frowned.
Although there is insufficient calculation time, the spin with mass loss field mentioned by Xu Yun cannot be calculated for a while.
But for him, a top quantum physics expert in the world, the form of the Lagrangian is not difficult to judge.
Based on simple analysis, he can roughly judge that the Lagrangian is in form...
There is indeed an extra negative sign.
This negative sign is not a purely mathematical negative number, but refers to negative energy.
Actually.
There is nothing wrong with simply having negative energy. There are some examples in theoretical situations where negative energy can be completely achieved.
For example, in the Casimir effect, when two uncharged metal plates are very close to each other, the suction force that occurs comes from the energy difference of the vacuum inside and outside the plates, and the vacuum between the plates has negative energy.
But the problem is that what we are constructing now is a loss field. Regarding the concept of loss field, there is a somewhat formal saying in particle physics to describe it, which is called:
Energy is not limited to the lower realm. E has a lower realm but no upper realm.
That is to say, the loss field situation with negative energy is not necessarily wrong, but it needs to be corrected, for example, by translating the field to obtain a point with lower potential energy, so as to obtain the real dynamic field equation, etc.
That is to say, this is a field that needs to be optimized.
More importantly...
In the calculation process of the KG field, if you want the energy to be negative, there is only one situation:
The space loss part is 0, and only the time component remains.
Thus.
It will also cause problems with the E-L equation and Hamiltonian density, and the Lorentz invariance will also be affected, eventually causing problems with the entire framework.
In other words...
In the situation mentioned by Xu Yun, there is indeed a possibility that the value of the pseudoquantity does not comply with the superposition commutative law.
Of course.
If you want to be truly confident, further calculations are needed.
Think of this.
Anton Salinger couldn't help but turn his head and look at Xu Yun, re-examined his nominal "disciple", and then said to Tehuft who rushed to his side again:
"Gerald, you have the best math skills among us, please excuse me."
Without further words, Tehuft understood what he was thinking:
"OK, leave it to me."
Finished.
The old man with a huge bald patch on his forehead picked up his pen and started doing calculations quickly.
Spins with mass loss fields belong to the category of quantized calculations, and the core is the plane wave solution of the E-L equation.
Then, by verifying that the z-axis is parallel to the direction of momentum, the completeness relationship is established. By adopting commutative quantization conditions for the three polarization losses, the spin with the mass loss field can be easily calculated.
Swish swish——
Because the data was complete, Tehoft's calculations were quick.
It only takes a few minutes.
He paused with his pen, raised his head and gave Anton Salinger a look of unknown meaning, then turned to Witten and said:
This chapter is not finished yet, please click on the next page to continue reading the exciting content! "Edward, Xu's statement is correct. According to our ideas, the spin of the gamut field is calculated to be 1/2."
"...."
In an instant, you could hear needles dropping all around you.
The cameraman at the scene cleverly narrowed the focus and captured the expressions of each elder at this time.
surprise,
Puzzled,
question,
anger,
At this time, different expressions appeared on the faces of scholars from different camps.
I said it dozens of lines above.
At present, there are only three types of elementary particle fields discovered in physics: scalar field, spinor field, and scalar field, all of which satisfy Lorentz symmetry.
The spinor field corresponds to particles with spin 1/2, which are 48 types of fermions.
The loss field corresponds to particles with spin 1, that is, 12 types of bosons.
In other words, the spin value of the delta field that can be described must be 1, and it can never be 1/2.
Still taking the Qidian boutique badge mentioned previously as an example.
The average subscription requirement for premium badges is 3,000 average subscriptions, that is, only books with an average subscription of 3,000 or more can enter the premium library.
In other words.
A book with 400 subscriptions cannot have a high-quality badge, nor can it be retrieved by the high-quality library.
A high-quality product is equal to or greater than three thousand uniformly, otherwise it is a non-high-quality product. This is an iron law - not only an iron law of the database, but also a concept that exists in the reader's cognition.
What Tehuft discovered at this time was equivalent to finding a novel with 400 subscriptions on a premium channel.
In this case, there may be something wrong with the eyes.
Either that...
An error occurred in the framework program for indexing books.
This situation combined with the current reality is...
Including Witten, the frameworks calculated by the other eight groups are not consistent with the characteristics of Pluto particles.
It’s not just Tehuft who realizes this, but also David Gross, Nima.
as well as......
Atsushi Suzuki.
Gulu——
The top boss from Neon swallowed hard and saw from the corner of his eye several cameras turning their lenses towards him...
Although there was no physical attack, he truly experienced what it meant to have a light on his back.
All the ridicule he had directed at Xu Yun before was now harshly reflected back on him.
clown......
It's me?
impossible!
Absolutely impossible!
A row of fine beads of sweat instantly appeared on Suzuki Atsushi's forehead. The old Baga, who looked as if he could belch at any time, began to think rapidly.
A few seconds passed.
He suddenly thought of something, and the decibel level of his voice increased a lot:
"Wait a minute! Mathematics is mathematics after all. Maybe the particles still obey the finite-angle loss-of-rotation basis on the physical level - there is precedent for this situation."
"For example, this is the case with the four-dimensional line element of mass in electrodynamics. After introducing certain variations, it still conforms to the mathematical formula. Who can guarantee that the particles will not be like this?"
Suzuki Atsushi's words aroused the approval of many people at the scene.
Some of these people do not want to lose face like this and are unwilling to admit failure in a hasty manner.
Some people simply agree with Suzuki Atsushi's statement.
After all, the development histories of the two disciplines of mathematics and physics are, in some sense, their respective histories of optimization and self-consistency.
Even in 2023, many physical phenomena still cannot be fully solved using mathematics, such as quantum collapse.
Just like what was said before.
Any physical phenomenon can eventually be described and explained using mathematics, but the node of this "explanation" may be very long.
Maybe decades ago.
Maybe decades later.
Maybe today.
Or it could be the next chapter...ahem, tomorrow.
So putting aside political overtones and personality, what Suzuki Atsushi said does have some truth to it.
Based on the current level of human mathematical development, pure mathematics cannot determine everything.
It is often the norm to first discover anomalies and then optimize and introduce the anomalies.
See this situation.
Witten couldn't help but glance at Atsushi Suzuki:
"So Mr. Suzuki, you mean..."
Suzuki Atsushi glanced back at him and waved his hand vigorously, as if to cheer himself up:
"The Fermi surface data of the Academy of Sciences group and our other eight groups are different, which means that the theoretical energy levels of the particles must also be different."
"So I think we can first determine the theoretical energy levels of particles under the two frameworks, and then..."
"Let's see at which energy level we can capture that particle!"
