The "mass gap" problem (also known as the mass gap problem) has always been the biggest obstacle to the "unification of physics", the ultimate theory that 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, quantum Yang-Mills equations in four-dimensional Euclidean space has a solution to the mass gap."

As mentioned before, in order to achieve the "unification of physics", it is necessary to find a unified theoretical framework that combines the only four basic forces that 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, and electromagnetic force can be described by Maxwell's equations (quantum electrodynamics (QED) after quantization). The strong and weak forces are both new "forces" discovered inside the nucleus and can only rely on quantum theory.

to explain.

What are "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 basic forces in the universe. It uses gluons to "stick together" quarks.

, thereby achieving a tight connection between protons and neutrons. The most well-known application example of the strong force is nuclear fission, which is the principle of making atomic bombs.

The weak force is also an interaction between various particles, using W, W-, Z0 and other particles called "bosons" as the transmission medium. Under the action of the weak force, neutrons can be converted into protons.

The weak force really comes into play when the nucleus decays, which is most obvious in beta decay. For example, carbon-14 decays into nitrogen-14 through weak interactions. The weak force of microscopic particles is the only thing that does not obey the conservation of parity.

In order to deepen the understanding of the strong and weak forces and ultimately achieve the unification of physics, quantum theory has developed into "quantum field theory" with the efforts of physicists. The most typical representative of this 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 commutative group (Abelian group) discovered by Weyl to the non-commutative group (non-Abelian group), so it is also called

Non-Abelian gauge field theory. The expanded non-Abelian gauge field theory can accurately describe the electroweak interaction and the strong interaction.

Through the precise mathematical framework provided by "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 interactions are almost completely determined.

The number of gauge bosons has also been completely determined, that is, undiscovered particles can be predicted directly from the strong force and electroweak theory. This makes the "Yang-Mills theory" the modern gauge field theory and the standard model of particle physics.

Foundation.

By the way, the weak force and electromagnetic force have now been completely unified (electroweak unified theory). After the unification, the electroweak force can also be described by the "Yang-Mills theory", that is to say, among the four basic forces

, except for gravity, the other three forces can be described by the "Yang-Mills theory". The significance of the "Yang-Mills theory" can be imagined.

As the "core of Yang-Mills theory", the "Yang-Mills equation" is also known as "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 big and thorny problem.

The classical version of the Yang-Mills equation describes a zero-mass wave propagating at the speed of light, but in quantum mechanics, each particle can be regarded as a special type of wave, especially the "strong" and "weak" forces.

There is a theoretical contradiction between the short-range force carried by particles with non-zero mass.

Are you a little confused by the above paragraph?

It doesn't matter, we will understand slowly. First we introduce a proper noun "boson" here.

The so-called bosons are particles that transmit forces, such as photons and gluons. In quantum field theory, each force has particles specifically designed to transmit forces. For example, photons transmit electromagnetic force, and strong particles transmit strong force.

It is a gluon, and what transmits the weak force is the W and Z bosons mentioned when introducing the weak force.

The issue of the mass of the boson is very important. The greater the mass of the boson, the shorter the force range (the distance the force is transmitted); the smaller the mass, the longer the force range; if the mass of the boson is zero, then the force range

It is infinitely far away, such as photons, so electromagnetic force can spread to very long distances.

The strong and weak forces are only limited to the nucleus, which means that 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 that the gauge boson has zero mass, but the short-range force facts of the strong and weak forces require that the corresponding gauge boson must have mass.

It is actually measured that W and Z bosons also have mass, and their mass is very large (the standard model of particle physics predicts that the mass of W boson should be 80357/-6 MeV/c2).

——This is the "big thorny problem" with theoretical contradictions just mentioned, the "mass gap" problem that has caused headaches to physicists and mathematicians all over the world. In mathematics, it is "Yang-Mills"

A special property of the solution of "Equation".

In order to solve this problem, the "Higgs mechanism" was proposed in physics, which is a mechanism for generating mass, that is, it enables elementary particles to gain mass. It believes that the universe is full of Higgs fields. If particles do not follow the

When the Higgs field interacts, its mass is zero (such as photons and gluons). If a particle interacts with the Higgs field, then it has mass. The stronger the interaction, the greater the mass obtained. 2012

In July of this year, scientists found the Higgs particle at the Large Hadron Collider (LHC), verifying this theory.

This chapter is not over yet, please click on the next page to continue reading! But the "Higgs mechanism" can only explain the weak W and Z bosons from a physical level, but it cannot explain why the strong gluons have zero mass.

Later, physicists made up for this problem through the "asymptotic freedom" property of "quantum chromodynamics".

Whether it is the "Higgs mechanism" or "asymptotic freedom", physicists have verified it through physical theoretical experiments and computer simulations, and thus determined a hypothesis - Bose when transmitting the strong and weak forces.

The particles (gluons and W and Z bosons) have mass, which also proves that quarks can only be part of composite particles 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" even though it has been verified by physics? Because this hypothesis cannot be explained or proven in mathematical language at present. It cannot be upgraded from a "hypothesis" to a "theorem" without being verified by rigorous mathematical theory.

Qin Ke and Ning Qingyun have been persevering in the past few months, constantly challenging this "mass gap" problem in order to turn this "hypothesis" into a "theorem".

After trying countless ways and methods, the two people's current idea is to deeply combine de Broglie's "matter wave" theory with "Yang-Mills's mass gap problem". They want to add the union with momentum mv,

Explain the existence of massless particles (such as photons) and mass particles (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 develop 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

The above explains how massless particles and particles with mass are related, and ultimately proves that in the Yang-Mills theory, there is a particle wave with a minimum mass greater than 0, which mathematically proves the existence of a mass gap.

This is a direction that the two of them feel is more feasible after repeated research, but they still encounter 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 mass particles changes. This is consistent with Mr. Yang's suggestion

The "parity non-conservation" is similar. Under the conditions of a weak mutual environment, the movement rules of theta particles and t particles will change - it is like two particles looking at a mirror, but the appearance they present is different from themselves.

not the same.

This unpredictable "change" gave both Qin Ke and Ning Qingyun a headache, and they could never find a suitable idea to accurately describe this "change" in mathematical language.

However, the "perturbation theory" mentioned by Academician Wang Heng inadvertently gave Qin Ke new inspiration, which was to introduce a new changing "constant" to describe this unpredictable "change".

"Yes, this idea should work!" Qin Ke wrote faster and faster, with the light of wisdom flashing in his eyes. Lines of complex mathematical calculations outlined a very beautiful trajectory, breaking away from several problems that have troubled the history of human mathematics.

After ten years of thick fog, the truth slowly emerged.

"L=1/4FμνF^μν 1/2M^2B^μ e^2νxB^μ ΓψφB2^η^2-φ(it^μΔ0m)φ..."

"It can be seen from the above equation that the SU3 group can be coupled to the complex scalar field φ set in Equation 29, which leads to φ=pe^iθ, and is converted to the gauge invariant combination Bμ≡Aμ-(1/e)xw

…”

"Applying to the Dirac Lagrangian function of Equation 22, assuming that a fluctuation constant term M=Yt is added, it can be substituted into Equation 67 to explain the spontaneous symmetry breaking..."

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

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

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

Like the most powerful swordsman, he rushes into the enemy formation and stabs every "difficulty" in his way with all his strength. Any one of these "difficulties" is enough for ordinary physicists to study for a lifetime and may not be able to solve it.

.

In the past few months, every little bit and every gain gained from jointly attacking the quality gap problem with Ning Qingyun has turned into strength for him to move forward.

It's getting closer, getting closer.

Qin Ke has seen the dawn of success slowly expand from a small point of light to a brilliant light, and the truth hidden in the fog has also revealed more and more true features...

However, the difficulty of the quality gap problem is too high, and the "inspiration amplification state" is even more exhausting. His forehead is already covered with sweat, and his face has changed from rosy to pale due to excessive mental exertion, as if he is undergoing

Like a marathon.

Qin Ke's expression was as determined as a rock from beginning to end. He pursed his lips and increased his writing speed as much as possible.

At this moment, there was nothing else in his mind except the "quality gap" issue.

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 feel as if he had been fished out of water, and his face became frighteningly pale.

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

Even the old academician Wang Heng came here several times to check on his disciple.

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

This chapter is not over yet, please click on the next page to continue reading! When he came to check on Qin Ke’s condition for the fifth time, Academician Wang Heng couldn’t help but asked Ning Qingyun in a low voice: “Xiao Ning, will anything happen to Qin Ke like this?

"

Ning Qingyun bit her red lips, tried hard to suppress the concern in her eyes, and whispered: "It's okay, it's fine this time. In the past, he ran two to thirty thousand meters before he started to get inspiration, and then he started to enter

Such a state of concentration.”

She said this, but she was extremely worried in her heart, because before, Qin Ke could only enter such a state of concentration for about half an hour at most, but now nearly three hours have passed. During this period, Qin Ke did not drink even a drop of water.

It is not over yet, and the current state is one that can be seen at a glance that it is at the end of its strength.

Will Qin Ke fall first, or will the quality gap be overcome first?

Ning Qingyun didn't know, so she could only clenched her fists hard, cheering and praying for Qin Ke.

Under everyone's nervous and worried gazes, Qin Ke's hand, which had become numb from writing, finally stopped.

He put down his pen, looked up at Ning Qingyun at the door, and grinned: "It's still a little bit short. I want to use mathematics to explain why gluons and W and Z bosons have mass, while photons transmit electromagnetic force.

But there is no quality... But I am too sleepy and can't keep up with my thinking, so it's up to you..."
To be continued...