638 Clever Proof Idea

Inst.i.tute of Physics.

Luo Wenxuan and Lu Zhou were standing side by side in front of a blackboard in the director’s office. They looked at the lines of equations on the blackboard and stood there silently for a long time.

Five minutes went by.

Luo Wenxuan suddenly broke the silence.

“I’ll get us something to drink?”

“Alcohol?”

“Yeah, it’s my habit. Whenever I can’t solve a problem, I’ll find something to drink”

“Then take a nap on the couch? Just throw the troublesome things aside?”

“Don’t say that… Do you really think I’m someone who does that?” Luo Wenxuan rubbed his nose and looked at the blackboard. He said, “Okay then, drinking aside, I suddenly remembered something.”

Lu Zhou: “What?”

“A thesis in Annual Mathematics, published in 1974… I don’t remember which page, but Witten showed it to me.” Luo Wenxuan recalled for a moment and said, “It mentioned a possible way.”

Annual Mathematics was one of the four big journals, and the theses inside were all authoritative.

Lu Zhou gave him the chalk and made an inviting gesture.

After Luo Wenxuan thought for a second and played around with the chalk, he walked up to the blackboard and began to write.

[The simplest case of energy density with standard order is λφ^4+φ2, where 0

Luo Wenxuan paused for a second and looked at Lu Zhou.

“The existence and uniqueness of the field have already been proven by the thesis author, I can find the thesis for you to look at.”

“Okay.” Lu Zhou nodded and said, “Continue.”

Luo Wenxuan turned around and continued to write while speaking.

“The ma.s.s of the field satisfies m=√(2+O(λ^3))

“Setting the subset ∏ to satisfy ∏Ω being dense in H, the existence of the ma.s.s gap depends on proving the following estimation… Which is, for any constant C, C < √2,=”” and=”” λ0=””>0. Also, the constant B of the operator A(A∈∏), for any 0←λ←λ0, has (AΩe^(-tH)·AΩ)←Be^(-tC), and is labeled as 1←t… ”

It took around five minutes for Luo Wenxuan to transfer the equations from his brain onto the blackboard.

“This is basically it. I’m not sure if there are any mistakes. I’ll take a look at the thesis later… Hey, why are you looking at me?”

“Nothing.” Lu Zhou looked away and shook his head. He said, “I’m just a bit surprised.”

Luo Wenxuan coughed and said, “I mean, I am Witten’s student.”

Lu Zhou: “Oh.”

Luo Wenxuan: “…”

Jesus, bragging to Lu Zhou doesn’t work at all.

Lu Zhou didn’t have time to care about Luo Wenxuan’s background. He stared at the equations on the blackboard for a minute.

Generally speaking, this proof idea was quite clever.

It took into account that the single-particle state was the eigenstate of the “ma.s.s” operator of the Hilbert s.p.a.ce, and the corresponding eigenvalue was the ma.s.s of the particle. According to special relativity, letting the speed of light be 1, the ma.s.s M, the energy H, and the momentum P of the exchange operator satisfy M^2 = H^2 – P^2.

This special case allowed the spectrum of M to be studied in more detail, and at the same time, the field ma.s.s M was an isolated eigenvalue in the spectrum M, and the corresponding eigenstate was the observed single-particle state. This was an irreducible representation transformation of the Poincare group.

Furthermore, the estimation formula (1) proved that for any ε>0 and sufficiently small λ, the ma.s.s gap Δ satisfied Δ>(√2-ε). This way, the whole problem became clear… At least, Lu Zhou thought so.

Lu Zhou thought for a bit before voicing his opinion.

“In theory, this proof should be feasible, but there are a few parts of the problem that need to be solved, like the particle… Or how the existence of ma.s.s M can’t be determined. You haven’t given a proof for that yet. Also, the asymptotic expansion of λ in √(2+O(λ^3)) isn’t written here.”

Luo Wenxuan was stunned, and he looked at Lu Zhou in disbelief.

“You’ve finished reading the whole thing?”

When Lu Zhou saw how surprised he was, he paused for a second before asking, “Is this supposed to be difficult?”

Luo Wenxuan said, “No… Not that difficult.”

It only took Luo Wenxuan five days to comprehend these equations.

Well, this thesis was actually quite simple compared to some of Witten’s other homework a.s.signments.

Luo Wenxuan comforted himself in his mind and returned to the main question at hand. He coughed and said, “The asymptotic expansion of the λ you just talked about, in the paper I mentioned, it provided a way to project the two ma.s.ses in a state in H by constructing a linear operator E2. We can prove that the existence of the operator E2 is a s.p.a.ce formed by a vector of the form of Ω and e^(-sH) Ω. As for the existence of the particle that proves the ma.s.s M… ”

He paused and awkwardly smiled.

“If I prove this, wouldn’t I win the Fields Medal?”

Lu Zhou: “…”

Luo Wenxuan’s words made sense, so Lu Zhou didn’t even know what to respond.

Even though this was a quantum chromodynamics problem, it was more specifically a complex mathematical proposition.

If someone could mathematically prove the existence of this particle, even if they couldn’t win a Fields Medal, they would at least win a Heinemann Mathematical Physics Award. Even though the latter had a lower status in the academic world and wasn’t comparable to the n.o.bel Prize, not to mention the prize money was only five thousand dollars, it was still highly respected in the world of mathematical physics. A lot of theoretical physics experts had won this award before.

For example, Weinberg, who founded the unified theory of electroweak interaction, won the award in 1977. He went on to win the n.o.bel Prize two years later.

If anyone could find the value of M or even observe the particle ma.s.s M…

It would definitely be worthy of a n.o.bel Prize.

While these two were silently thinking, an Inst.i.tute of Physics researcher walked in.

He looked at the equations on the blackboard and was muddled. He even began to have doubts about his life.

Who am I?

Where am I?

What the h.e.l.l are these things on the blackboard?

He ignored the things written on the blackboard and gently knocked on the door.

“Professor Lu, there is someone outside the inst.i.tute looking for you.”

Lu Zhou kept staring at the blackboard. “Who?”

The researcher said, “He claims to be the owner of Zhongshan New Materials, I think his name is Liu Wanshan.”