638Clever Proof Idea
Institute of Physics.
Luo Wenxuan and Lu Zhou were standing side by side in front of a blackboard in the directors 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.
Ill get us something to drink?
Yeah, its my habit. Whenever I cant solve a problem, Ill find something to drink
Then take a nap on the couch? Just throw the troublesome things aside?
Dont say that Do you really think Im 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 dont 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 ^4+2, 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 mass of the field satisfies m=(2+O(^3))
Setting the subset to satisfy being dense in H, the existence of the mass gap depends on proving the following estimation Which is, for any constant C, C < 2,= and= 0=>0. Also, the constant B of the operator A(A), for any 00, has (Ae^(-tH)A)Be^(-tC), and is labeled as 1t
It took around five minutes for Luo Wenxuan to transfer the equations from his brain onto the blackboard.
This is basically it. Im not sure if there are any mistakes. Ill 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, Im just a bit surprised.
Luo Wenxuan coughed and said, I mean, I am Wittens student.
Lu Zhou: Oh.
Jesus, bragging to Lu Zhou doesnt work at all.
Lu Zhou didnt have time to care about Luo Wenxuans 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 mass operator of the Hilbert space, and the corresponding eigenvalue was the mass of the particle. According to special relativity, letting the speed of light be 1, the mass 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 mass 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 >0 and sufficiently small , the mass gap satisfied >(2-). This way, the whole problem became clear At least, Lu Zhou thought so.Read more chapter on vipnovel.com
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 mass M cant be determined. You havent given a proof for that yet. Also, the asymptotic expansion of in (2+O(^3)) isnt written here.
Luo Wenxuan was stunned, and he looked at Lu Zhou in disbelief.
Youve 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 Wittens other homework assignments.
Luo Wenxuan comforted himself in his mind and returned to the main question at hand. He coughed and said, The asymptotic expansion of the you just talked about, in the paper I mentioned, it provided a way to project the two masses in a state in H by constructing a linear operator E2. We can prove that the existence of the operator E2 is a space formed by a vector of the form of and e^(-sH) . As for the existence of the particle that proves the mass M
He paused and awkwardly smiled.
If I prove this, wouldnt I win the Fields Medal?
Luo Wenxuans words made sense, so Lu Zhou didnt 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 couldnt 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 wasnt comparable to the Nobel 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 Nobel Prize two years later.
If anyone could find the value of M or even observe the particle mass M
It would definitely be worthy of a Nobel Prize.
While these two were silently thinking, an Institute 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 hell 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 institute 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.