"It's easier to explain the coupling of spin and charge in the system. I've sent you the relevant concepts, and you should know that the introduction of similar algebraic structures can capture the key physical properties of the system more accurately by establishing more complex operator relationships."
Xu Changshu asked with a look of surprise, "I know that, but the last manuscript you sent seemed to lack a specific quantitative analysis. Also, have you completed the proof of your transcendental geometry?"
Qiao Ze nodded and replied, "Almost. I've been working on the appropriate extension of the system's Fock space lately. I have now reconstructed the model on a one-dimensional chain. Specifically, by introducing the superoperators A_j and B_j, representing electrons with spin up and spin down at position j, respectively. Then, the basic relation of Super Helical Space Algebra is actually very simple: [A_jB_j = -B_jA_j]."
"Next, using the concepts of transcendental geometry, through the Berry curvature and Chern number, one can obtain the expression for Berry curvature F. The key is the subsequent analysis of spin-orbit coupling and topological phase transitions. I need to find and introduce a suitable interaction to ensure that the coupling term can lead to a topological phase transition, thus affecting the system's mass gap."
"Once that issue is resolved, I'll be able to prove the phase transition of the mass gap by adjusting the parameters in the superspiral space algebra and the strength of the spin-orbit coupling terms. Thus proving the existence of the mass gap. The problem itself isn't hard, it's just that the computation is vast, but I've already simplified it, and now I'm waiting for the supercomputer's results."
"As long as the supercomputer ultimately gives a result that could, when inputted, allow the equation [V = \\sum_j (A_jB_j + h.c.)] to hold, my paper will be concluded," Qiao Ze said lightly.
Although Qiao Ze spoke easily, Xu Changshu's eyes had already widened in astonishment, "Wait, are you saying that your method of proof is by showing that the mass gap can be adjusted to prove its existence?"
The response of the professor who had switched jobs puzzled Qiao Ze, prompting him to ask, "Is there a problem?"
Xu Changshu exclaimed, "No, there's no problem. But does this mean your findings can be directly validated in the lab?"
"Isn't that a good thing? Mathematics, in a sense, serves physics," Qiao Ze replied.
At a loss for words, Xu Changshu felt a tinge of envy for contemporary physicists; he really hadn't seen a mathematician like Qiao Ze...
"No, it's great, but you've practically spoon-fed those high energy physicists. If someone could use your theory to find corresponding evidence in the lab first, they could easily snag a Nobel Prize in Physics," Xu Changshu said.
Qiao Ze shook his head, "It's not that simple. Mental calculations alone tell us that the instantaneous energy required for validation is enormous, and the experiment itself would consume a vast amount of resources. Plus, the occurring process is extremely short-lived, so finding a pattern amidst the complex signals is quite challenging."
Xu Changshu clearly had a different point of view: "Of course, it's hard to find without a reference, but if one goes searching with a purpose, perhaps analyzing previous signals from colliders might yield something."
Qiao Ze smiled and made no comment.
If his work came to fruition, it would just be a Nobel Prize—after all, he wasn't the one who'd be issuing the prize money, was he?
If it could indeed be verified in physics, that would actually be a good thing, potentially saving him a lot of time in the future.
So he casually asked, "Anything else?"
"Uh... no, that's it!" Xu Changshu hesitated for a moment, then shook his head.
Sorry, old boss, but he really didn't know how to bring this up with Qiao Ze anymore.