Institute of Physics.

In the director's office, Lu Zhou and Senior Brother Luo stood side by side in front of a blackboard, looking at the scribbled lines of calculations on the blackboard, and were silent for more than ten minutes without speaking.

About another five minutes passed.

Luo Wenxuan suddenly broke the silence.

"Can I go get some wine?"

"Wine?"

"It's my habit, whenever I have a problem that I can't figure out, I'll go find something to drink."

"And then lie on whose arm and take a nap? By the way, put the troublesome things aside first? ”

"Don't say that...... Am I that kind of person? With a dry cough, Luo Wenxuan touched his nose, stared at the blackboard and continued, "Okay, put aside the matter of wine first, just now I suddenly remembered something. ”

Lu Zhou: "What came to mind?" ”

"An article in Annals-of-Mathematics, 1974 edition...... I can't remember how many pages I can't remember, but it was Witten who asked me to read them," Luo Wenxuan continued, "There is a possible way to do it. ”

"Annals-of-Mathematics" is also known as the Annals of Mathematics, as one of the four top journals, and the articles on it are still very authoritative.

Lu Zhou handed the chalk to him and made a gesture of please.

Luo Wenxuan didn't refuse, stood in front of the blackboard and thought for a moment, gently threw the chalk in his hand, and then stepped forward to write.

[The simplest case of energy density with standard order is λφ^4+φ??, where 0<λ "1......]

When writing this, Luo Wenxuan paused and looked back at Lu Zhou.

"The existence and uniqueness of this field has been proven, and I can turn to the paper to show you later."

"Okay," Lu Zhou nodded, "Go ahead." ”

Luo Wenxuan turned around and continued to write on the blackboard as he spoke.

“…… The mass of the field satisfies m=√(2+O(λ^3))"

"Let the subset of operators ∏ satisfy the ∏Ω that the existence of the mass gap is dependent on proving the following estimates...... That is, for any Changshu C, satisfying C0, and a constant B that depends on its operator A(A∈∏), and for any 0←λ←λ0, there is (AΩe^(-tH)· AΩ) ←Be^(-tC), for 1←t...... Marked by Eq. (1)"

It took about five minutes for Luo Wenxuan to write down the content of his memory on the blackboard and looked back at Lu Zhou.

"That's basically it, I'm not sure if there's anything missing, I'll go back and dig out that document and read it...... Uh, why are you looking at me like that? ”

"It's nothing," retracting his surprised gaze, Lu Zhou shook his head, "I just feel a little surprised." ”

Luo Wenxuan coughed lightly and reminded, "I also graduated from Witten. ”

Lu Zhou: "...... Oh. ”

Luo Wenxuan: "......"

Damn, I really don't even have a chance to pretend to be a force.

Ignoring those inconsequential things for the time being, Lu Zhou stared at the equation on the blackboard for about a minute.

Overall, there is something clever about this line of proof.

Considering that the single-particle state is the eigenstate of the "mass" operator in Hilbert space, the corresponding eigenvalue is the mass of the particle. According to the special theory of relativity, under the unit system with the speed of light of 1, the mass M and the energy H and momentum P as exchange operators satisfy M?? =H?? -P??。

In this special case, it is allowed to study the spectrum of M in more detail. At the same time, the field mass m is an isolated eigenvalue in the spectrum of M, and the corresponding eigenstates are the observed single-particle states, which in turn are irreducible representation transformations of the Pangjialai group.

Coupled with the fact that estimation Eq. (1) proves that for an arbitrary ε>0 and sufficiently small λ, there is a mass gap Δ satisfying Δ>(√2-ε), and the whole problem becomes clear...... At least in Lu Zhou's opinion.

After thinking for a while, Lu Zhou gave his own evaluation.

Theoretically, this idea of proof should be possible, but there are still a few problems to be solved, such as the particle ...... Or that the existence of mass m cannot be determined, at least you don't give proof here. There is also an asymptotic expansion of λ in m=√(2+O(λ^3)), which is also not given here. ”

As soon as he heard this, Luo Wenxuan was suddenly shocked, and looked at Lu Zhou in disbelief.

"You're done?"

Seeing the surprised expression on his face, Lu Zhou was slightly stunned and asked rhetorically.

"Is it hard?"

Luo Wenxuan Khan said: "Also...... It's not that hard. ”

It would have taken him four or five days at most to understand this thing......

Well, compared to the other "homework" assigned by the old man Witten, this one is indeed relatively simple.

After comforting himself in his heart, Luo Wenxuan stopped interrupting, returned to the original topic, coughed lightly and continued.

"The asymptotic expansion of λ you mentioned gives a method in the literature I mentioned, by constructing an asymptotic projection linear operator E2 on H, and projecting the state in H on a state less than the mass of two particles, it can be proved that there is an operator E2 whose range is a space stretched by vectors of the shape Ω and e^(-sH) Ω. As for what you said about proving the existence of particles of mass m......"

At this point he paused, and smiled a little embarrassedly.

"If I had proven it, I wouldn't have won the Fields Medal sooner?"

Lu Zhou: "......"

It made so much sense that he didn't even know how to complain.

Although this is a quantum chromodynamics problem, it involves a complex mathematical proposition.

If the existence of this particle can be proved mathematically, even if you don't win the Fields Medal, you can win a Heinemann Prize in Mathematical Physics. Although the latter's status in the academic world is not as good as the Nobel Prize, and the prize money is only a pitiful $5,000, the force in the field of mathematical physics is still quite high, and many bigwigs engaged in theoretical physics research have won this award.

For example, Weinberg, who created the unified theory of weak electricity, won the prize in 1977 (and soon won the Nobel Prize two years later).

As for who can find the value of m, even observe this particle with a mass m......

A Nobel Prize will definitely not be able to run away.

Just as the two fell silent, a research assistant from the Institute of Physics walked in.

When he saw the content on the blackboard, he was stunned for a while, and subconsciously doubted his more than ten years of life with the discipline of physics.

Who am I?

Where am I?

What's written on this blackboard?

It took a while to come back to his senses, forcibly ignoring the books written on the blackboard, and he knocked lightly on the open door and said.

"Professor Lu, someone outside the research institute is looking for you."

Lu Zhoutou, who was staring at the blackboard, didn't ask back: "Who?" ”

The researcher continued: "He claims to be the boss of Zhongshan New Materials, and his name seems to be Liu Wanshan. ”

Genius one second to remember the address of this site:. Mobile version reading URL: m.