Chapter 300 - 272: The Best at Gauge Field Theory Isn’t in the Group Chat
"Also, I want to let everyone know something first."
"I won’t be spending a lot of time with the group myself."
"We’ll... probably meet about once a month."
The moment he said this,
a quiet murmur spread through the room.
"Once a month?"
"Isn’t East God going to be with the group full-time?"
"So when he’s not with the group... what’s he going to be doing?"
"If we only meet once a month, who’s actually in charge of this group?"
"..."
The voices weren’t loud.
It was mostly just a few of the newly accepted PhD students whispering among themselves.
Li Dong naturally heard them too.
He understood, of course.
He knew what a creature like a PhD student feared most in a large research group like this.
It wasn’t having a supervisor who was too strict.
It was having a supervisor who was never around.
For a doctoral student still fumbling their way through a major research topic, that was a truly terrifying prospect.
The relationship between a PhD student and their project was like a string.
The other end of this string was held in the supervisor’s hand.
As long as the supervisor was present, someone was pulling the string.
But for the newly accepted PhD students in this room, who held their strings?
It wasn’t Wang Zhigang.
It wasn’t Liu Ruochuan.
It was Li Dong.
Li Dong had proposed the conjecture.
Li Dong had drawn the map.
Ultimately, how to cap the proof was still Li Dong’s call.
And yet, the first thing Li Dong told them was:
"’I’ll be gone a lot, so you guys will have to figure things out on your own.’"
To a new PhD student, this statement was equivalent to the person holding their string stuffing it into someone else’s hands and walking away.
It was inevitable they would feel insecure.
The professors on the other side of the table reacted much more calmly than the students.
But that didn’t mean they were completely without their own doubts.
They had all led their own research groups.
They had all seen other people’s groups, too.
But not a single one of them had ever seen a group like this.
The group’s central figure, meeting with them only once a month.
...
However, Wang Zhigang, Liu Ruochuan, and Penrose didn’t share this particular doubt.
The three of them approved of this arrangement.
The reason was simple.
No one in this room could keep up with Li Dong’s train of thought.
If Li Dong were really with the group full-time,
this room full of PhD students and professors would most likely have nothing to do.
Li Dong would finish everything by himself.
And there would be no need for the group to exist.
So, Li Dong’s current arrangement was actually for the best.
He would provide the direction.
He would build the skeleton.
The rest of the group would fill in the flesh.
The PhD students would fill in their part.
The master’s students would fill in theirs.
The professors would gather around this skeleton and each claim a rib or two.
Perhaps in the intervals between the monthly meetings, a few new, smaller projects would emerge from the main lines of the grander direction.
These smaller projects...
Each one could potentially become a paper in *Annals*.
Each one could allow a PhD student to graduate early.
It might even propel a second-tier professor into the first tier.
This was an opportunity Li Dong was intentionally leaving for them.
But the three professors wouldn’t spell this out.
They had to figure it out for themselves over time.
...
After he finished speaking, Li Dong considered adding a few words of encouragement.
But he thought about it and swallowed the words back down.
He wasn’t the type of person who was particularly good at inspiring others.
Forcing it would just seem pretentious.
He clasped his hands in a traditional gesture of respect to everyone in the room.
"That’s all for today."
"As for the specifics, Professor Wang will make the arrangements."
"That’s it for now."
...
He nodded to the professors again and turned to walk out the door.
He was in a hurry.
He hadn’t finished walking down that little path of physics in his mind.
Teacher Wu hadn’t given him much time.
So he needed to erect the κ framework for the WKB approximation as quickly as possible.
As Li Dong pushed the door open and left,
a few of the PhD students inside were still muttering.
"Once a month..."
"Is that really going to work?"
「Dorm 404.」
When Li Dong pushed the door open, he froze for a second.
Someone was actually in the room.
"Huh?"
"Haozi, you’re in the dorm today?"
On the top bunk,
Wang Hao was lying on his side, holding a book.
Hearing Li Dong enter, he looked over with a resentful expression.
"Gu God."
He bit out the two words coldly.
"He went to interview for your research group."
Li Dong froze.
’Right.’
’Gu Ming came for an interview today.’
Li Dong laughed guiltily.
Wang Hao couldn’t be bothered with him.
WHOOSH. He rolled over, turning his back to Li Dong, and went back to his book.
Li Dong shook his head and didn’t disturb him further.
He sat down at his own desk.
What he had to do now...
was to take that κ from his stack of morning draft paper—the one that Teacher Wu’s comment, "the source is empty," had exposed...
and give it a physical origin that wasn’t based on inversion.
Li Dong first drew a dotted line down the center of his draft paper.
Above the dotted line, he wrote two words.
[Vacuum Stage]
To the right of the dotted line, he wrote a simple formula.
Under the WKB approximation, the tunneling probability is written as exp(-2∫κ(z)dz).
κ(z) = √(2m·(V(z)-E))/ℏ.
Everyone knew how to write this part.
But after this point, the path diverged.
The path on the left was inversion.
The path on the right was calculating V(z) from fundamental physics.
And Li Dong had to take the path on the right.
He lowered his head and began his derivation.
Step one: break V(z) into three parts.
The part for the tip.
The part for the vacuum.
The part for the Au(111) substrate plus the Ligand Field.
Step two: use the work function of the tip material and the tip’s geometry to provide a phenomenological approximation.
Step three: use the image potential between the electron from the tip and the sample to provide an analytical form.
Step four...
When he reached the fourth step, Li Dong paused.
The fourth step was the Au(111) substrate plus the Ligand Field.
What he had to do in this part was simple.
He needed to correlate the effective action of the electric dipole operator in this section with the phase selection of the transition matrix.
In short...
he had to rewrite that line from the morning, [φ=0], from being a hard-coded mathematical constraint into a natural physical conclusion.
But he got stuck on something he never expected to get stuck on.
The real representation of the dipole operator under the three sets of basis vectors.
He had thought this would be straightforward.
The dipole parity selection rule gives a real sign.
That was something even a high school physics student would know.
But the problem was...
when you needed to strictly apply this real sign to the transition function between the three sets of basis vectors,
you didn’t just need an isolated sign.
Instead...
you needed to write this real sign onto the non-Abelian local group structure where the U(1) electromagnetic gauge is coupled to the atomic orbital parity symmetry.
In other words...
he needed to take the U(1) gauge invariance of the electromagnetic field, the discrete parity of the atomic orbitals, the local C₃v symmetry of the Au(111) substrate...
and incorporate all of these things into a single, unified gauge structure.
Li Dong tried writing a couple of equations.
He got halfway through and crossed them out.
He tried another approach.
Starting from C₃v and coupling towards U(1).
He got to the third line and crossed it out again.
"This part."
Li Dong put down his pen.
A feeling he hadn’t had in a long time washed over him.
He didn’t understand it!
Li Dong rubbed his temples.
’This thing... how do I even tackle this?’
’Do I start by taking the semidirect product of the electromagnetic U(1) and the parity Z₂?’
’Or should I go with the non-Abelian Berry connection route?’
’If I write out both, which one is physically correct?’
"..."
He muttered to himself for a while.
Finally, he leaned back in his chair and stared at the ceiling.
’This part... I can’t figure it out on my own.’
’I need to ask someone.’
But who could he ask?
The experts in the group chat?
The problem was...
the most brilliant person in gauge field theory—someone who could see through all this miscellaneous stuff like U(1), parity, and orbital symmetry at a glance and effortlessly break it down into the cleanest set of equations for you—wasn’t in the group chat...
He was at Shuimu!