I really just want to be a scholar

The "mass gap" problem (also known as the mass gap problem) has always been the biggest obstacle in the way of the ultimate theory of "physical unification", which is regarded as the holy grail of modern physics.If described in mathematical language, this problem can be described as: "For any compact, simple gauge group, the quantum Yang-Mills equations in four-dimensional Euclidean space have a mass-gap solution."

As mentioned earlier, in order to realize the "unification of physics", it is necessary to find a unified theoretical framework, which combines the four basic forces that only exist in nature, namely electromagnetic force, gravity, strong force (strong nuclear force, strong interaction force) ) is unified with the weak force (weak nuclear force, weak interaction force).

At present, gravity can be described by general relativity, electromagnetic force can be described by Maxwell’s equations (quantum electrodynamics QED after quantization), and both strong force and weak force are new “forces” found inside the nucleus, which can only rely on quantum theory to explain.

What is "strong" and "weak"?
Specifically, the strong force mainly acts between particles, so it is often called the "strong nuclear force". It is the strongest of the four known fundamental forces in the universe. It "sticks" each quark together through gluons , so as to realize the close connection between protons and neutrons.The best-known example of the application of force is nuclear fission, the principle behind which the atomic bomb is made.

The weak force is also an interaction between various particles, and the particles called "bosons" such as W+, W-, and Z0 are used as the transmission medium.Under the action of the weak force, neutrons can be transformed into protons.The weak forces really come into play when nuclei decay, most notably in beta decay, such as carbon-14 decaying to nitrogen-14 through weak interactions.The weak force of microscopic particles is the only existence that does not obey parity conservation.

In order to deepen the understanding of the strong and weak forces and finally realize the unification of physics, quantum theory has developed into a "quantum field theory" with the efforts of physicists. The most typical representative is Mr. Yang and Mills in 1954. The "Yang-Mills Theory" and its core equation "Yang-Mills Equation" proposed by Mr.

The greatest significance of "Yang-Mills theory" is that it extends the gauge theory (applied to electromagnetic theory) of the exchangeable group (Abelian group) discovered by Weyl to the non-commutative group (non-Abelian group), so it is also called Non-Abelian gauge theory.The extended non-Abelian gauge field theory can accurately describe the electroweak and strong interactions.

Through the precise mathematical framework provided by the "Yang-Mills theory", as long as a certain symmetry (corresponding to a group in mathematics) is selected, or as long as a certain group is determined, the subsequent interaction is almost completely determined, it The number of gauge bosons in is also completely determined, that is, the undiscovered particles can be predicted directly from the strong force and electroweak theory.This makes the "Yang-Mills theory" the basis of modern gauge field theory and the Standard Model of particle physics.

By the way, the weak force and the electromagnetic force have now been completely unified (unified theory of electroweak force), and the unified electroweak force can also be described by the "Yang-Mills theory", that is, among the four basic forces , except gravity, the other three forces can be described by "Yang-Mills theory", and the significance of "Yang-Mills theory" can be imagined.

The "Yang-Mills equation", which is the core of the "Yang-Mills theory", is therefore called "the key equation for quantum field theory to conquer the grand unified theory of matter".

But when physicists unify the electromagnetic force and the weak or strong force through the "Yang-Mills equation", they encounter a thorny problem.

The classical version of the Yang-Mills equation describes a zero-mass wave traveling at the speed of light, but in quantum mechanics each particle can be viewed as a special type of wave, and in particular the "strong" and "weak" forces are composed of There is a theoretical contradiction between the short-range force carried by particles with non-zero mass.

The above paragraph is a bit confusing?

It's okay, we slowly understand.First of all, we introduce a proper term "boson" here.

The so-called bosons are particles that transmit force, such as photons and gluons.In quantum field theory, each force has a particle that is dedicated to transmitting the force. For example, photons transmit the electromagnetic force, gluons transmit the strong force, and W mentioned above when introducing the weak force. and the Z boson.

The quality of the boson is very important. The larger the mass of the boson, the shorter the force path (distance of force transmission); the smaller the mass, the longer the force path; if the mass of the boson is zero, then the force path It is infinitely far away, such as photons, so the electromagnetic force can propagate to a very long distance.

Both the strong force and the weak force are only limited in the nucleus, that is to say, the force range is very short, and the boson has a large mass.

But the problem is that in the "Yang-Mills theory", the local gauge symmetry requires the gauge boson to be zero-mass, but the fact of the short-range force of the strong force and the weak force requires that the corresponding gauge boson must have mass, It is actually measured that the W and Z bosons also have mass, and the mass is very large (the standard model of particle physics predicts that the mass of the W boson should be 80357+/-6 MeV/c2).

——This is the "tough big problem" just mentioned that there are theoretical contradictions, and the "mass gap" problem that has caused headaches for physicists and mathematicians all over the world.In mathematics, it is a special property of the solution of the "Yang-Mills equation".

In order to solve this problem, the "Higgs mechanism" is proposed in physics, which is a mechanism for generating mass, that is, it can make elementary particles acquire mass.It believes that the Higgs field is everywhere in the universe. If a particle does not interact with the Higgs field, its mass is zero (such as photon, gluon), and if the particle interacts with the Higgs field, then it will be There is mass, and the stronger the effect, the greater the mass obtained. In July 2012, scientists found the Higgs particle at the Large Hadron Collider (LHC), confirming this theory.

But this "Higgs mechanism" can only explain the weak W and Z bosons from the physical level, but it cannot explain why the strong gluons have zero mass. Later, physicists solved this problem through "quantum chromodynamics" The "asymptotically free" feature of .

Whether it is the "Higgs mechanism" or "asymptotic freedom", physicists have verified it through physical theory experiments and computer simulations, and thus determined a hypothesis - Bose when transmitting strong and weak forces The gluons (gluons and W and Z bosons) have mass, which also verifies that the quarks can only be part of the compound and cannot exist alone.

This hypothesis is described in physical language, that is - for vacuum excitation, there must be a "mass gap" of strong interaction, that is, there is a non-zero minimum energy level (that is, there cannot be a particle wave with a mass of 0).

Why is it still called a "hypothesis" after it has been physically verified?Because at present, this hypothesis cannot be explained or proved in mathematical language.Without a rigorous mathematical theory to verify, it is impossible to upgrade from a "hypothesis" to a "theorem".

In the past few months, Qin Ke and Ning Qingyun have also been persistently and continuously challenging this "quality gap" problem, in order to turn this "assumption" into a "theorem".

After trying countless ways and methods, the two people's current thinking is to deeply combine De Broglie's "matter wave" theory with "Yang-Mills' mass gap problem", and want to combine it with the momentum mv, Explain the existence of massless particles (such as photons) and particles with mass (such as gluons) together, and then make a breakthrough from the objective existence logic of elementary particles.

One of the key points here is to study a "union formula" in group theory. As long as the existence of this "union formula" is proved, new non-Abelian groups can be continuously derived on this basis. From mathematics Explain how massless particles are related to particles with mass, and finally prove that in the Yang-Mills theory, there is a particle wave with the smallest mass and greater than 0, which also proves the existence of a mass gap mathematically.

This is already a direction that the two of them found to be more feasible after repeated research, but they still encountered many difficulties.

One of the most critical ones is the uncertainty and nonlinearity of the union formula, which will always produce unpredictable "changes" as the "relationship" between massless particles and particles with mass changes, which is consistent with Mr. Yang's proposal It is similar to the "parity non-conservation" that comes out. Under the condition of weak mutual environment, the motion law of the θ particle and τ particle will change-this is like two particles looking in the mirror, but the appearance and itself are different. not the same.

This unpredictable "change" caused headaches for both Qin Ke and Ning Qingyun, and they couldn't find a suitable way to accurately describe this "change" in mathematical language.

However, the "perturbation theory" mentioned by the old academician Wang Heng inadvertently gave Qin Ke a new inspiration, that is, to introduce a new "constant" of change to describe this unpredictable "change".

"That's right, this idea should work!" Qin Ke wrote faster and faster, with the light of wisdom in his eyes, and the lines of complex mathematical formulas outlined a very beautiful trajectory, breaking away from the history of human mathematics that has troubled several times. Ten years of thick fog slowly revealed the truth.

“L=1/4FμνF^μν+1/2M^2B^μ+e^2νχB^μ+ΓψφB2^η^2-φ(iτ^μΔ0m)φ……”

"From the above formula, it can be seen that the SU3 group can be coupled to the complex scalar field φ set in formula 29, and thus φ = ρe^iθ, and converted to obtain the gauge invariant combination Bμ≡Aμ-(1/e)χω ..."

"Applied to the Dirac Lagrangian function in formula 22, assuming that a fluctuation constant term M=YΤ is added, it can be substituted into formula 67 to explain the spontaneous symmetry breaking..."

Qin Ke wrote faster and faster, sparks of thinking kept popping up in his mind, and inspiration erupted.

Quantum chromodynamics, quantum electrodynamics, and even the standard particle model... Qin Ke seemed to be roaming in the ocean of knowledge, and powerful pleasure and excitement flowed through his body, making him extremely excited.

Sheets of snow-white manuscript paper were filled with writing and then moved to the side. Many of them fell directly from the desk, but Qin Ke didn't notice it at all.

He is like the most powerful swordsman, rushing into the enemy's formation, stabbing the "difficulties" that block the way with all his strength, and any of these "difficulties" are enough for ordinary physicists to study for a lifetime, but they may not be able to solve them. .

In the past few months, every bit of the joint attack on the quality gap problem with Ning Qingyun, every bit of gain, has been transformed here into his strength to move forward.

It's getting closer, it's getting closer.

Qin Ke has seen the dawn of success slowly expand from a small spot of light to a brilliant light, and the truth hidden in the mist is also revealing more and more of its true face...

But the difficulty of the quality gap problem is too high, and the "Inspiration Amplification State" is extremely exhausting. His forehead is already covered with sweat, and his face has changed from the original rosy to pale due to excessive energy consumption, as if he is undergoing an exercise. Like a marathon.

Qin Ke's expression was as firm as a rock from the beginning to the end. He pursed his lips and tried to increase his writing speed as much as possible.

At this moment, he had nothing else in his mind except the "mass gap" problem.

After an unknown amount of time, Qin Ke's body began to tremble unconsciously due to excessive exhaustion, and his clothes were soaked with sweat, making him look as if he had been fished out of the water, and his face was even more frighteningly pale.

Ning Qingyun and Qin Xiaoke, who were worried, had already quietly pushed open the door of the study, and looked at him worriedly at the door.

Even the old academician Wang Heng came over several times to check on the situation of his disciple.

But no one dared to disturb Qin Ke. Qin Ke was extremely exhausted but extremely excited at this time, obviously he had a very crucial inspiration.

When he came to check on Qin Ke's situation for the fifth time, the old academician Wang Heng couldn't help asking Ning Qingyun in a low voice: "Xiao Ning, will something happen to Qin Ke like this?"

Ning Qingyun bit her red lips lightly, tried to suppress the concern in her eyes, and said in a low voice, "It's okay, this time it's already fine, before he started to get inspired after a long-distance run of [-] to [-] meters, and then started to enter Such a state of focus."

She said this, but she was extremely worried in her heart, because Qin Ke entered such a state of concentration before, at most it took about half an hour, but now it has been nearly three hours. Not yet, and the state at this time is even more obvious at a glance that it is at the end of its battle.

Did Qin Ke fall first, or was the quality gap problem overcome first?
Ning Qingyun didn't know, so she could only clenched her fists tightly, cheering and praying for Qin Ke.

Under the nervous and worried eyes of everyone, Qin Ke's hand that had been numb from writing finally stopped.

He put down his pen, looked up at Ning Qingyun at the door, and grinned: "It's a little bit close, I want to use mathematics to explain why gluons, W and Z bosons have mass, and photons that transmit electromagnetic force But it has no quality... But it's too sleepy, and I can't keep up with my thinking, so it's up to you..."

After he finished speaking, he staggered to a wooden chair next to him, fell down slowly, and fell into a deep sleep in the next second.

Ning Qingyun hurried over to wipe Qin Ke's sweat with a handkerchief, but Qin Ke was completely soaked and had to change clothes.

"Xiao Ning, is Qin Ke alright?" Senior Academician Wang Heng asked his son Wang Hua to come help, and asked with concern.

"He just fell asleep from exhaustion. It happened several times before. It's okay. You don't have to worry." Ning Qingyun told Qin Xiaoke who wanted to come over to help: "Xiaoke, help clear all the manuscripts on the ground first." Pick it up." Then he asked Teacher Wang Heng: "Teacher, can I borrow a set of clothes for Qin Ke to change?"

"I have clean spare clothes!" Wang Hua had just arrived, and together with Wei Feng who also rushed over, they picked Qin Ke up and moved them to a more comfortable room.

After hurriedly changing clothes for Qin Ke and settling down again, everyone returned to the study.

Qin Xiaoke has already sorted out all the manuscript papers, but she doesn't understand the mathematics, so the order may be a bit messy: "Sister-in-law... Maybe you need to rearrange the order."

Ning Qingyun responded, and searched with trembling hands, and soon found the last page.

See the top half of the last page, it says—

"It is thus proved that for any compact, simple gauge group, the quantum Yang-Mills equations in four-dimensional Euclidean space have a mass-gap solution."

Ning Qingyun just felt an indescribable pride and joy flowing all over her body. Her favorite prince of mathematics has opened a heavy door in physics and mathematics again!

Even the old academician Wang Heng couldn't hide his excited expression. He gently took the manuscript paper, with tears in his eyes, and murmured: "Qin Ke, this kid... is amazing! Three hours! Another world-class math problem fell on him. It's written!"