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?
As we all know.
In physics, two basic particles can be divided according to large classifications, which are the so-called fermions and bosons.
Fermions are particles that follow Fermi-Dirac statistics, including electrons, protons, neutrons, etc.
Fermions have a half-integer spin and comply with the Pauli exclusion principle, which means that 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 forces.
Bosons have integer spin and are not restricted by the Pauli exclusion principle. Multiple bosons can be in the same quantum state.
Of course.
In this early era of physics, the scientific community's understanding of these two particles was far from as complete as it would be in later generations.
Among them, fermions are relatively well understood. After all, particles such as protons and neutrons have been discovered for many years, and have even given birth to many Nobel Prizes directly or indirectly.
But bosons are much lighter.
The concept of boson was first proposed by Dirac. At that time, he gave this particle the name boson in order to commemorate the contribution of Indian physicist Satyendra Nath Bose.
The most typical understanding of bosons in this era is photons, and that's it.
That’s right, there will be no follow-up.
Therefore, when Xu Yun proposed [gauge boson with vector], Zhao Zhongyao and others not only did not suddenly realize it, but were a little confused.
After a while.
Zhao Zhongyao and Hu Ning looked at each other, organized their speech slightly, and asked Xu Yun:
"Xiao Han, what do you mean by the vector gauge boson...?"
"Could it be said that in addition to vector bosons, there are also scalar bosons?"
Xu Yun nodded towards him and affirmed:
"That's right."
Zhao Zhongyao frowned immediately, but he did not interrupt Xu Yun's rhythm.
Based on his past experience in dealing with Xu Yun.
Although Xu Yun often throws out some concepts that are not surprising, but no matter how beyond the current understanding of these concepts, Xu Yun will give a relatively detailed explanation of them, and almost never throw out concepts.
But the principle is not given.
This is also the reason why so many experts in the base accepted Xu Yun so quickly - it's not a big problem if the theory is shocking, as long as a reasonable explanation can be given.
At present, the level of instruments in this period is quite primitive, and theorists are basically the same as the lobbyists in ancient times. Those who can refute and persuade others are the top strategists.
as expected.
Xu Yun didn't show off much this time, but quickly picked up a pen and wrote a formula on the paper;
ds2=c2dt2?dx2?dy2?dz2=ημνdxμdxν.
Then Xu Yun drew a line under the formula and said to Zhao Zhongyao:
"Director Zhao, this is a standard Min space-time line element, with an RΛ4 linear space and a Min metric ημν with a sign difference of 2." (Who can tell me how to use the fourth power Sogou...
.)
"If we make the assumption that the operator of a single-particle state only depends on the position and velocity at the delay time, 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."
Anyone who was Lorenz’s classmate in a previous life should know this.
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 you only need to consider the properties of the group.
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 boss like Zhao Zhongyao, so Zhao Zhongyao quickly wrote down the corresponding steps:
"Let's start with the momentum operator, p^=?i?dd...."
"When the annihilation operator acts on the ground state, it gets zero, that is, a?ψa=0, and the factor?2?mw can be reduced..."
"Then we make a dimensionless conjugate complex amplitude operator, and its time evolution is multiplied by the eiwt phase change..."
More than ten minutes later.
Zhao Zhongyao gently put down his pen and showed a thoughtful expression:
"Huh... there are actually two analytical solutions to the harmonic oscillator?"
Then he looked at Hu Ning and Zhu Hongyuan, who were calculating at the same time, and asked:
"Lao Hu, Comrade Hong Yuan, what's your result?"
Hu Ning raised the calculation paper in his hand towards him:
"I also have two solutions."
Zhu Hongyuan’s answer is equally concise:
"Me too."
Seeing this situation, Lao Guo couldn't help but squint his eyes.
What he calculated was the particle number operator of the 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 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.
The corresponding value in field theory for spin zero is...
Scalar concept.
This is actually easy to understand.
The natural units used in quantum field theory are used for calculations. The speed of light in vacuum c=reduced Planck constant?=1, and the space-time coordinates x=(x?,x?,x?,x?)=(x,y
This chapter is not finished yet, please click on the next page to continue reading the exciting content! The energy-momentum relationship of the special theory of relativity is E2= P2 m2, let the energy E be replaced by the energy operator i?/?t, and the momentum P be replaced by the momentum operator
By replacing ?i▽, you can get -?2/?t2=-▽2 m2, that is, ▽2-?2/?t2-m2=0
Let both sides act on the wave function Ψ to get (?2-m2)Ψ=0. This is the famous Klein-Gordon field equation.
The operator ?2 is a four-dimensional scalar under Lorentz transformation, that is, ?'2=?2 The square of the rest mass m2 is a constant.
To make the Klein-Gordon field equation covariant with the Lorentz transformation, the space-time coordinates of the equation (?2-m2)Ψ=0 are subjected to the Lorentz transformation to obtain (?'2-m2)Ψ'=0
The form remains unchanged, and the only requirement is that the wave function Ψ'=Ψ after Lorentz space-time coordinate transformation can achieve the purpose. Such a field is called a scalar field.
If the Lorentz transformation is made special, keeping time constant and rotating in space, then the rotated wave function Ψ'(X',t)=exp(-iS·a)Ψ(X,t).
This means that when time t remains unchanged, the space coordinate vector
And the wave function Ψ(X,t) becomes exp(-iS·a)Ψ(X,t)=Ψ'(X',t), and Ψ(X,t)=Ψ'(X',t)
.
The only way is to set 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 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. He took a deep breath and calmed down before continuing to look at the third-party report in Wang Ganchang's hand.
If you take into account the influence of vector bosons...
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 others summarized.
In a sense, this explanation is even a bit... boring?
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.
There are two analytical solutions calculated by Zhao Zhongyao under the guidance of Xu Yun, corresponding to vector bosons and scalar bosons respectively.
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 gauge field theory is photon, which is true at least in electromagnetic interaction.
Nowadays, gauge bosons have been extended to weak force or strong force, and the trend is quite normal.
Just like when you usually read an online novel, the author originally used real-time jokes. The incident happened either today or yesterday, and everyone was making fun of it [following current events without saving the manuscript].
As a result, it was suddenly discovered that the author's jokes were no longer timely and occurred 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 longer than three days, but the trend is not difficult to accept.
But the scalar boson is somewhat beyond the readers' logical acceptance range - it is equivalent to the author saying that he has 200,000 manuscripts in hand, and it is enough for the readers not to complain about telecommunications fraud...
Zhao Zhongyao is in such a situation right now. He really can't figure out how a writer who writes 4,000 words a day can have 200,000 manuscripts...
However, the expression of Xu Yun opposite him was very calm. After deciding to kick him out, he didn't hesitate much:
"Director Zhao, I wonder what your understanding of bosons is?"
"What do I know about bosons?"
Hearing Xu Yun's rhetorical question, Zhao Zhongyao was slightly startled at first, and then replied:
"Of course it is a particle that transmits force. It is similar to two people throwing a ball. The gauge boson is the ball."
Xu Yun nodded slightly, without commenting on whether Zhao Zhongyao's words were correct 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...that is, the ball. So where does the mass of the person who throws the ball...come from?"
"quality?"
Zhao Zhongyao repeated this word, and after a few seconds, his pupils suddenly shrank!
quality.
This is a very important property in the field of particles.
In the macroscopic world, all macroscopic objects are composed of atoms, which are composed of atomic nuclei and extranuclear electrons.
Relative to the mass of the nucleus, the mass of the electron (0.511MeV) can be ignored.
For macroscopic substances, their mass can be considered to be concentrated on the nucleus.
But the micro field is different.
For example, the atomic nucleus is composed of positively charged protons and uncharged neutrons, and there are "meta-hadrons" within the protons and neutrons. The transfer of force between these particles has been described, but the mechanism for imparting mass
But it's still blank.
And quality cannot appear out of thin air, so this mechanism has always been a very cutting-edge theoretical exploration area.
Unfortunately, no one has ever been able to come up with a reasonable explanation, either domestically or internationally.
But right now it seems...
Could it be that the scalar boson deduced by Xu Yun and Zhao Zhongyao has this possibility?
This chapter is not over yet, please click on the next page to continue reading! Then Xu Yun thought for a while, marked an area with the palms of his hands in front of him, and said:
"Director Zhao, you should know that in the relativistic quantum theory, because the energy is extremely high, the creation and annihilation of particles can be considered 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 the theory of relativity, 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 we followed Einstein's idea of general relativity and wrote the derivatives in the Lagrangian quantity as covariant derivatives, and we got the new Lagrangian quantity - the consequence of this is that a vector field is inevitably introduced."
"Under the corresponding specification restrictions, the simplest model of this vector field is the electromagnetic field."
This time, Lu Guangda, who was beside Zhao Zhongyao, nodded first.
Xu Yun's words are not unfamiliar to him. His friend Yang Zhenning originally came up with 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, the Yang-Mills field has a big drawback, that is, the model has no quality - so Mr. Yang... ahem, the achievement that Mr. Yang Zhenning won the Nobel Prize for was not the Yang-Mills field, but the universe.
It’s called nonconservation.”
"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 just finished speaking.
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 more updates tomorrow and will keep adding them until the end of the month. The average number is 8,374 words per day. In total, 8,400 is easy to say....
