walk into unscientific

"Gauge bosons for .vectors?"

Hearing Xu Yun's words.

Zhao Zhongyao and others, who had originally focused on Xu Yun, couldn't help but subconsciously froze, and now there was a hint of confusion.

what does this mean?
Well known.

In physics, there are two kinds of elementary particles that can be divided according to the classification, namely the so-called fermions and bosons.

Among them, fermions are particles that follow Fermi-Dirac statistics, including electrons, protons, neutrons, and so on.

Fermions have a half-integer spin, which conforms to the Pauli exclusion principle, that is, there cannot be two or more fermions in the same quantum state.

Bosons are particles that follow Bose-Einstein statistics, including photons, W bosons, Z bosons, Higgs bosons, etc. They are the basic particles that constitute force.

Bosons have integer spins, which are not limited by Pauli's exclusion principle, and multiple bosons can be in the same quantum state.

Of course.

In today's early era of physics, the scientific community's understanding of these two particles is far from being as perfect as later generations.

Among them, fermions are relatively well understood. After all, particles such as protons and neutrons have been discovered for some years, and have even given birth to many Nobel Prizes directly or indirectly.

But bosons are much shallower.

The concept of boson was first proposed by Dirac. At that time, in order to commemorate the contribution of Indian physicist Satyendra Nath Bose, he named this particle a boson.

The most typical cognition of bosons in this era is photons, and then nothing more.

That's right, there will be no follow-up.

Therefore, when Xu Yun proposed [gauge bosons with vectors], Zhao Zhongyao and others not only did not suddenly realize it, but were a little confused.

After a while.

Zhao Zhongyao and Hu Ning at the side looked at each other, organized their words a little, and asked Xu Yun:

"Xiao Han, what do you mean by vector gauge boson?"

"Could it be that in addition to vector bosons, there are also scalar bosons?"

Xu Yun nodded to him, affirming:

"Yes."

Zhao Zhongyao frowned immediately, but he didn't interrupt Xu Yun's rhythm.

According to his past experience in dealing with Xu Yun.

Although Xu Yun often throws out some concepts that are not astonishing and endless, no matter how these concepts are beyond the existing cognition, Xu Yun will give them a more detailed explanation, and almost never throws out concepts. But don't give a rationale for the situation.

This is also the reason why so many experts in the base accepted Xu Yun so quickly—it’s not a big problem to make a theoretical statement, as long as a reasonable explanation can be given.

At present, the level of equipment in this period is quite primitive, theorists are basically no different from ancient lobbyists, and those who can refute and persuade others are top strategists.

as predicted.

Xu Yun didn't show off much this time, but quickly picked up a pen and wrote down a formula on paper;
ds2=c2dt2dx2dy2dz2=ημνdxμdxν。

Then Xu Yun drew a line under the formula and said to Zhao Zhongyao:

"Director Zhao, this is a standard Min's time-space linear element, which has an RΛ4 linear space, and is equipped with a Min's metric ημν with a sign difference of +2." (Who can tell me how Sogou fights to the fourth power.)

"If we make an assumption that the operator of the single-particle state depends only on the position and velocity at the delay moment, can you make an irreducible unitary representation of the SO(3) group?"

"."

After hearing this, Zhao Zhongyao thought for a few seconds and quickly touched his chin:

"it should be OK."

Students who were Lorenz in the previous life should know it.

In the free field scenario, the Lorentz transformation does not change the form of the field. The matrix D determines the transformation method of the field, so only the properties of the group need to be considered.

And W is a small group. For a massive particle field, if you want to make an irreducible unitary representation of the SO(3) group, you only need to consider the annihilation operator on the right.

This kind of calculation is not a difficult problem for a big guy like Zhao Zhongyao, so Zhao Zhongyao quickly wrote down the corresponding steps:

"Let's start with the momentum operator, p^=idd"

"When the annihilation operator acts on the ground state, zero is obtained, that is, aψa=0, and the factor 2mω can be reduced"

"Then make a dimensionless conjugate complex amplitude operator, and its time evolution is to multiply the phase change of eiωt"

After ten minutes.

Zhao Zhongyao gently put down his pen and showed a thoughtful expression:

"Huh, the harmonic oscillator actually has two analytical solutions?"

Then he looked at Hu Ning and Zhu Hongyuan, who were calculating at the same time, and asked:

"Old Hu, Comrade Hong Yuan, what's your result?"

Hu Ning raised the counting paper in his hand to him:

"I also have two solutions."

Zhu Hongyuan's answer is equally concise:
"Me too."

Seeing this situation, Lao Guo couldn't help squinting his eyes.

What he calculated is the particle number operator of SO(1) and SO(3) groups. Although the precondition is that the operator of the single particle state only depends on the position and velocity at the delay time, this assumption is almost the same as the reality. .

And it is displayed according to the calculation results.

This model has two analytical solutions mathematically, corresponding to the bosonic gauge field described in quantum.

One of the analytical solutions corresponds to a spin of 1, and the other analytical solution corresponds to a spin of 0.

And the spin of zero corresponds in field theory to
Scalar concept.

This is actually quite understandable.

The natural unit used in quantum field theory is used for calculation, the speed of light in vacuum c=reduced Planck’s constant=1, the space-time coordinates x=(x,x,x,x)=(x,y,z,it) =(X, it), partial differential operator = (,,,) = (/x, /y, /z, /it) = (, -it) = (▽, ​​-i/t)
The energy-momentum relation of special relativity is E= P+ m, let the energy E be replaced by the energy operator i/t, and the momentum P be replaced by the momentum operator i▽, then we can get -/t=-▽+ m, that is, ▽- /tm=0
Let both sides act on the wave function Ψ to get (-m)Ψ=0, which is the famous Klein-Gordon field equation.

The operator is a four-dimensional scalar under the Lorentz transformation, that is, '=the square of the rest mass m is a constant.

To make the Klein-Gordon field equation have the covariance of the Lorentz transformation, that is, the form of ('-m)Ψ'=0 obtained after the Lorentz transformation of the equation (-m)Ψ=0 space-time coordinates remains unchanged, The only requirement is that the wave function Ψ'=Ψ after the Lorentz space-time coordinate transformation will achieve the goal, and such a field is called a scalar field.If the Lorentz transformation is special, keep the time constant and rotate in space, the wave function after rotation Ψ'(X', t)=exp(-iS·α)Ψ(X, t).

That is to say, when the time t is constant, the space coordinate vector X of the wave function Ψ(X, t) turns into a vector X' after rotating an infinitesimal α angle in the direction of the angular momentum S.

And the wave function Ψ(X,t) becomes exp(-iS·α)Ψ(X,t)=Ψ'(X',t), and Ψ(X,t)=Ψ'(X',t) .

The only way is to let the spin angular momentum S=0, which means that the field particle spin described by the Klein-Gordon field equation is zero.

Very simple and very easy to understand.

In other words.
Bosons can indeed be divided into scalar bosons and vector bosons as Xu Yun said.

"."

After a while.

Zhao Zhongyao's chest rose and fell slightly, and he took a deep breath. After calming down, he continued to look at the third-party report in Wang Ganchang's hand.

If the influence of vector bosons is considered.
It is not difficult to explain the abnormal final state of the hadron:

Hadrons are also a typical composite particle, and the structure of a vector gauge boson inside is completely reasonable—this is also a type of "meta-hadron" that Zhu Hongyuan and his colleagues have summarized.

In a sense, this explanation is even a bit dull?

However, Zhao Zhongyao did not feel bored by this boring explanation. At this time, his curiosity was surprisingly strong:

"Xiao Han, what exactly is the scalar boson you are talking about?"

mentioned above.

Under the guidance of Xu Yun, Zhao Zhongyao calculated two analytical solutions, corresponding to vector bosons and scalar bosons.

Among them, although the vector boson is somewhat beyond Zhao Zhongyao's current knowledge, it itself falls within the category that can be understood after knowing the truth.

After all, there is a concept in quantum field theory called gauge symmetry, which is gauge field theory.

The typical representative of the gauge field theory is the photon, which is at least established in the electromagnetic interaction.

Now the gauge boson extends to weak force or strong force, and the trend is normal.

It's like you usually follow an online novel. Originally, the author was playing with real-time meme. The event happened either today or yesterday.

As a result, it was suddenly discovered that the author's joke was no longer timely, and it happened for more than three days. Then readers would naturally suspect that the author had saved manuscripts for more than three days.

As for gauge bosons, it is equivalent to the author admitting that he has a manuscript for seven days.

This time span is more than three days, but it is not difficult to accept the trend.

But the scalar boson is a bit beyond the logical acceptance range of readers-it is equivalent to the author saying that he has 20 manuscripts in his hand, and it is enough for readers not to complain about telecom fraud
Zhao Zhongyao is in such a situation right now. He really can't figure out how an author who writes 20 words a day can have [-] manuscripts.
However, Xu Yun opposite him had a very calm expression, and he didn't hesitate much after deciding to kick the jio:
"Director Zhao, what is your understanding of bosons?"

"What do I know about bosons?"

Hearing Xu Yun's rhetorical question, Zhao Zhongyao was startled for a moment, and then replied:
"Of course it is the particle that transmits force, similar to two people throwing a ball, and the gauge boson is the ball."

Xu Yun nodded lightly, without evaluating whether Zhao Zhongyao's words were right or not, but continued:

"In that case. Director Zhao, have you thought about a question?"

Zhao Zhongyao glanced at him:
"what is the problem?"

Xu Yun raised a finger:
"There is a medium for the transmission of force, which is the ball. So where does the mass of the person who throws the ball come from?"

"quality?"

Zhao Zhongyao repeated the word, and after a few seconds, his pupils shrank violently!
quality.

This is a very important property in the particle realm.

In the macroscopic world, all macroscopic objects are composed of atoms, and atoms are composed of atomic nuclei and extranuclear electrons.

Relative to the mass of the nucleus, the mass of the electron (0.511 MeV) is negligible.

So for macroscopic substances, their mass can be considered to be concentrated on the nucleus.

But the microscopic realm is different.

For example, the atomic nucleus is composed of positively charged protons and uncharged neutrons, and there are "meta-hadrons" inside the protons and neutrons. The force transfer between these particles has been described, but the mass-imparting mechanism But it's still blank.

And quality cannot appear out of thin air, so this mechanism has always been a very cutting-edge theoretical research area.

Unfortunately, no one has ever been able to come up with a reasonable explanation, both domestically and internationally.

But right now.
Xu Yun guided Zhao Zhongyao to deduce this kind of scalar boson, does it have this possibility?
Then Xu Yun thought for a while, drew an area with the palms of both hands, and said:

"Director Zhao, you should know that in the quantum theory of relativity, because the energy is extremely high, the generation and annihilation of particles can be regarded as inevitable phenomena."

"This phenomenon leads to the non-conservation of the number of particles in the system, so a field with infinite degrees of freedom is introduced as the starting point of quantization."

"At that time, we were considering a complex scalar field that satisfies the covariance of relativity theory, so we required the Lagrangian quantity of the field to be as simple as possible. That is to say, the Lagrangian quantity of the complex scalar field does not change after it is multiplied by the factor exp."

"Then imitating Einstein's idea of ​​general relativity, write the derivative in the Lagrangian as a covariant derivative, and then get a new Lagrangian - the consequence of doing this is that a vector field will inevitably be introduced."

"The simplest model of this vector field is the electromagnetic field, under the corresponding gauge constraints."

This time, Lu Guangda beside Zhao Zhongyao nodded first.

Xu Yun's words are not unfamiliar to him. His good friend Yang Zhenning got the Yang Mills field based on this idea.

However, the Yang-Mills field of this era has no mass like the electromagnetic field and cannot describe short-range interactions.

Then Xu Yun glanced at Lu Guangda, and continued:
"As we all know, there is a big disadvantage of the existence of the Yang Mills field, that is, the model does not have quality-so Mr. Yang. Keke, Mr. Yang Zhenning's achievement in winning the Nobel Prize was not the Yang Mills field, but the parity. conservation."

"But on the other hand, if a new idea is introduced, the Yang-Mills field can become a very perfect theoretical and mathematical base."

Xu Yun's voice just fell.

Lu Guangda couldn't help but swallowed his saliva and asked impatiently:

"What idea?"

Xu Yun was silent for a few seconds:

"Consider a degenerate vacuum."

Note:
I will start adding updates tomorrow and continue until the end of the month, with an average of 8374 words per day, so 8400 is easy to say.