Chapter 639 Ingenious Proof Ideas

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 a few lines of calculations scribbled on the blackboard, and fell silent for more than ten minutes without speaking.

About five minutes passed.

Luo Wenxuan suddenly broke the silence.

"Can I go get some wine?"

"liquor?"

"This is my habit. Whenever I encounter a problem that I can't figure out, I will find something to drink."

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

"Don't say that... am I that kind of person?" With a dry cough, Luo Wenxuan rubbed his nose, stared at the blackboard and continued, "Okay, let's put aside the alcohol thing, just now I suddenly remembered something thing."

Lu Zhou: "What did you think of?"

"A paper on "annals-of-mathematics", the 1974 edition...I don't remember exactly how many pages, Witten let me read it at the time," Luo Wenxuan continued after recalling carefully for a while, "It contains Here's a possible way."

"Annals-of-mathematics" is also the Annual Journal of Mathematics. As one of the four top journals, the articles on it are still very authoritative.

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

Luo Wenxuan didn't refuse. He stood in front of the blackboard and thought for a moment, lightly tossed the chalk in his hand, and then walked 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 have been proven, and I can turn to that paper for you later."

"Okay," Lu Zhou nodded, "Go ahead."

Luo Wenxuan turned around and continued to write while talking on the blackboard.

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

"Assuming that the operator set ∏ satisfying ∏Ω is dense in H, the existence of the mass gap depends on proving the following estimation...that is, for any Changshu C, satisfying C<√2, the existence constant λ0>0, and depending on its The constant B of the operator A (A∈∏), for any 0←λ←λ0, has (AΩe^(-tH)·AΩ)←Be^(-tC), for 1←t... marked as formula (1 )”

It took about five minutes for Luo Wenxuan to write what he remembered on the blackboard, and turned to look at Lu Zhou.

"Basically, that's all. I'm not sure if I missed anything. I'll look up that document when I get back... Uh, why are you looking at me like that?"

"It's nothing." Lu Zhou retracted his unexpected gaze, and shook his head, "I just feel a little surprised."

Luo Wenxuan coughed lightly and reminded, "I also graduated from Witten's school."

Lu Zhou: "...Oh."

Luo Wenxuan: "..."

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

Leaving aside those irrelevant things for now, Lu Zhou stared at the calculations on the blackboard for about a minute.

In general, this line of proof does have its ingenuity.

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

In this particular case, the spectrum of M is allowed to be studied 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, and these states are an irreducible transformation of the Poincarai group.

In addition, the estimation formula (1) proves that for any ε>0 and sufficiently small λ, there is a mass gap Δ that satisfies Δ>(√2-ε), and the whole problem has become clear at a glance... At least in Lu Zhou's view so it is.

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

"Theoretically, this line of proof should be feasible, but there are still a few problems to be solved, such as the particle... or the existence of the mass m cannot be determined, at least you have not given a proof here. Also about m The asymptotic expansion of λ in =√(2+O(λ^3)) is also not given here."

Upon hearing this sentence, Luo Wenxuan was startled and looked at Lu Zhou in disbelief.

"Have you finished watching?"

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

"is it hard?"

Luo Wenxuan said sweatingly: "It's...not too difficult."

In order to understand this thing, it took him four or five days at most...

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

So 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, a method is given in the document I mentioned. By constructing a linear operator E2 of asymptotic projection on H, the state in H is projected to less than two In the state of a particle mass, it can be proved that the value range of the operator E2 is the space spanned by vectors of the shape Ω and e^(-sH)Ω. As for the proof of the existence of the particle with mass m... ..."

When he stopped here, he smiled a little embarrassedly.

"If all this is proven by me, wouldn't I have won the Fields Medal early?"

Lu Zhou: "..."

What he said was so reasonable that he didn't know how to complain.

Although this is a problem in quantum chromodynamics, it is actually a complex mathematical proposition involved.

If the existence of this particle can be proved mathematically, even if you can't get the Fields Medal, you can still get a Heinemann Prize in Mathematics and Physics. Although the latter's status in academia is not comparable to that of the Nobel Prize, and the prize money is only a pitiful five thousand dollars, it is still quite high in the field of mathematical physics. Many bigwigs engaged in theoretical physics research have won this award .

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

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

A Nobel Prize will definitely not escape.

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 ten years of life with physics as a subject.

who I am?

where am I?

What is written on this blackboard?

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

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

Lu Zhou stared at the blackboard without answering, "Who?"

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