@SillyGoose as an aside it is called a principal bundle

@ACuriousMind yeah technically the solution is the principal bundle itself with a connection satisfying the EOM

In fact you get sum over different bundles when considering instantons for example

@lucabtz oh gosh thanks

how should i draw the u-channel?

with memes

i just exchanged 1 and infinity in the end

r u doing string theory

Miao

@lucabtz you asserted that the channel names come from the pictured pant decompositions, but it does not seem at all obvious why they should be named that way. Are these the Mandelstam s t u variables?

@Mr.Feynman M I A O ~

@naturallyInconsistent yeah think of them of string scattering diagrams

thank its the s t and u channels like in feynman diagrams

anyhow its just a naming scheme it isnt so important

@lucabtz then you should not be making that claim in that caption. Because nobody should be expected to deduce that the diagrams should make the naming convention obvious.

@lucabtz I am aware of enough basic string theory lore to admire the basic premise and hate how it is oversold.

@naturallyInconsistent i think the people who are interested in the paper will understand, ive seen people naming them s t and u without even giving a reason for it

@lucabtz but they are most likely not trying to make the claim that you are. They are simply asserting that in their drawing schemes, those are what those 3 channels correspond to

They are not attempting to reason out a convention...

@naturallyInconsistent they dont really draw

they just call them $L_s$, $L_t$ and $L_u$

Then they are making even less of an effort...

anyhow the drawing is just explaining which pant decompositions are relevant for each definition

The $s$-, $t$- and $u$-channels correspond to the above pant decompositions of the four-punctured Riemann sphere. The blue curve is where the two pair of pants are glued together, which also correspond to the monodromies used in the definitions of $L_{0t}$, $L_{01}$ and $L_{t1}$. Notice in the last picture $1$ and $\infty$ are exchanged

maybe like this is clearer without trying to assert that there is a logic behind the names

then somebody will understand that in fact there is a logic, but whatever it is really unimportant

Do we have a confirmation of the naming of the Mandelstam variables? It seems to be suggesting that s is the "s"quare of the occuring energy, t is the 4-momentum "t"ransfer, and that the two of them happened to be in order of the alphabet, so it was picked for the next letter, u, to be used

@lucabtz much better~

@naturallyInconsistent thanks

utterly detest that this would have improved some string theory paper, but if it is for you, I shalt tolerate it

tsundere maximus

@naturallyInconsistent its okay i dont really like string theory much even if i do it

i mean i like it because a lot of qft stuff has very nice constructions and interpretations in string theory but i dont think in its current state it can describe anything real

also at this point what is considered string theory is so broad that it is difficult to not be doing it when you are in hep-th or math-ph

when did ya'll learn gauge theory o.0

@SillyGoose in my masters

abelian gauge theory was done in QFT II

non-abelian in standard model (but only the classical bits) and advanced QFT (with the quantum bits like Faddeev Popov, BRST and some bits on Batalin Vilkovinski)

man oh man

and supersymmetric gauge theory in susy and with a lot of self study for thesis

y do gauge fields show up in nature

it almost seems like one would not be able to even do high energy theory at phd and beyond without doing a masters

I mean...that's why you do a masters before a PhD? :P The US idea that you can put people into a "PhD program" right after a bachelor's degree is very weird from a European viewpoint

@SillyGoose never

but also the kind of "gauge theory" you're doing right now is more than the vast majority of physicists ever learn

Also, don't assume that physicists who have studied gauge theory are familiar with bundles

@ACuriousMind it is very weird also from an american point of view...

there's no bundles or connection forms or horizontal subspaces or whatever in most physics texts dealing with gauge theory

i think some people who really knew they wanted to do academia early on in the states apply to phd programs and master programs and defer their phd a year so they can do the masters

i have sharpened my focus to just trying to understand the "holonomy of a connection" within the next two weeks...

@SillyGoose The American style of having a PhD right after BS is actually that they have combined both a MS and PhD into one gigantic 7-year long slog, whereas in the EU system, the BSc covers more, the MSc is only one year, whereas the USA BS is much less than the EU BSc, so that their MS is 3 years, to make up for the difference. Every part of this is created by necessity, due to a series of unfortunate realities

@SillyGoose The only gauge the usual physicist ever learns, in Maxwell's equations, and even there, people just throw Coulomb gauge at it and forgets about it.

@naturallyInconsistent hm i guess so, but at the program i am going to the required coursework is not too many courses (at least it seems so; this may be an anomaly, though). also, i am not doing hep-th :P maybe such students would just take more courses or independent studies

Hello Everyone...

gauge theory is extremely important for standard model

Hello @RyderRude

@SillyGoose it has very very very little to do with "required coursework". Like, basically, who cares? As long as the student that comes out of a well-thought-out course ends up being actually able to do research, nobody cares. Instead, what is much more likely to happen, is that institutional malaise and fistfights in the curriculum planning arena end up with courses that are basically impossible for students to navigate, and important concepts are just lost to the æther.

@123 hello

@naturallyInconsistent the masters are two years long here in italy

@lucabtz Most MSc actually end up between 1.5 years and 2 years. 1 year is an ideal only for geniuses.

@naturallyInconsistent no here its two years even if you are a genius

meowth

the European ("Bologna") standard fixes bachelor degrees to be 3-4 years and master degrees to be 1-2 years with a total time of 5 years; many countries implement this as 3 years bachelor and 2 years master

you cant finish it quicker than that, the first graduation session is after 2 years that you started

yeah im literally in university of Bologna lol

My country has 4 years graduation and 2 years masters.

@ACuriousMind since pizza and pasta are such important staples of student diets, it stands to reason that the Italians also set the standards there.

Bologna was just the place where the treaty for this was negotiated :P

But we have school till 10th standard, then we go to the college for 2 years for intermediate 12th standard. Then 4 years bachelors and 2-2.5 years masters

bolognese yum yum

independent study can be betr than university sometimes

because u can learn things on the internet

the modern philosophy of free will attempts to re concile it with physics and neuroscience

@ACuriousMind maybe because we are the oldest university in the western world

anyone want to play this? lichess.org/fLcQScN2

@naturallyInconsistent

@naturallyInconsistent in the UK MSc is one year, and students usually do graduate in one year. In the rest of Europe MSc are mostly two-year degrees. It's not really comparable, the UK basically ignored Bologna

@imbAF if you can even obtain solutions that are of the form, of position function alone multiplied by time function alone, then it is a stationary state.

@fqq I know, I did my degree there...

@imbAF still called the same thing. It is not very useful to have separate concept for that

or name

Ok, and while I know that the time component, doesn't affect the probability density function, i.e the norm

what is physically different between

$\phi(\vec r)$ and $\phi(\vec r)\chi(t)$?

one is not a full solution of the full Schrödinger's equation, the other one is. However, once you have the solution of TISE, then it is trivial to obtain the eigenvalue and thus get the full solution. Trivial, so no good reason to really distinguish them

bye for now

aha

ok thanks

a cloud weighs a million tonnes

Does anyone know about the kauffman bracket in physics?

My professor said that the kauffman bracket and related constructions allow you to obtain the jones polynomial that jones originially obtained via tqft constructions