/sci/ - Science & Math

I made this one question up, but once it was clear that you can set up a theory of real observables via symmetric (hermitian) objects even if the spaces involved are inherently complex, Wigner already 2 years after the Schrödinger equation wrote down SO(3) actions for any dimension
https://en.wikipedia.org/wiki/Wigner_D-matrix

Of course the 6 dimensions of the electromagnetic field are somewhat of a ruse, since the [math]F_{E,B}[/math] is closed and you can describe the situation with a 1-form. The whole setup of the electromagnetic field comes with the spin-1 representation of the rotation group, for example.

That's the group action part of the story. To be explicit here, the dimensions of the Lie group (10 for Poincare resp. Galilean, or 6 for just Lorentzian resp. homogeneous Galilean) is not what the fields end up having. You don't assign group elements to fields. The groups, with its possible action on any object in physical space, captures coordinate transformations, but the representation map also determines the object type on which said action acts. The representation theory classifies the objects on which the group can act in principle, and those which further can be compressed into a real L are of physical interest to you.

There's not all that many field theories in the classical framework which are considered good description of the world on a classical level, so given the lack of examples maybe it's moot to ponder what it would mean to stack such fields and ride on the "semi-simple" point. The simplest situation is that were we got our standard fields from, I can only say that empirically.

As I said, the "particle" thing comes only into play once you talk about quantum field theory.

***The integral in the action-principle can technically also stomach some total derivatives, which end up being classified by the cohomology theory of the group in question, some notes here

https://youtu.be/IYBY0qe01x8

>>8418558
Probably nothing that would really interest you.
I write a Python GUI and API that controls a lab with superconducting qbits and I do the statistical evaluation ("data science") of accident track record of the Viennese police.
I think about physical units and try to rewrite foundations avoiding Joules or any mention of "energy".
A friend is teaching me some 20th century philosophy and another one is doing a space start-up.
For this and other reasons I want to get more into optimization in numerics and a bit mechanics.
Now I want to read the Probabilistic Robotics book (>>8418462) and then the Idris one.
My foundations are more constructive than yours. Then again, this thread was mine (>>8403989) too.

>>8416383
Go here (>>8418462) and learn/teach/discuss. Thanks!
Some probability basics are up next, then I'll see where to go.
The book actually says in chapter one that jumping from chapter 2 (Probability theory and other math necessities) to chapter 7 (Mobile Robot Localization: Markov and Gaussian) is a valid option, at least for teaching

>>8096425
It's a sort of Pie/Strudel.

They are mostly sweet, but that one is with Spinach

https://de.wikipedia.org/wiki/Strudel_%28Gericht%29

(the girl at my lab cooks one for us each week for a Game Of Thrones night)

>>7583410
do you always get rustled this easy?

>>7459729
Indeed, I was not saying you shouldn't move around. It looks good on a CV and, what's more important, living independently forms you. I know that I've changed a whole lot in the last 4 years, while not even crossing a language barrier.
I'm just warning you that most other cities - to me - are small and nothing is going on or gray and busy. Vienna isn't lacking intelligent people and has culture. It's a non-creepy version of Berlin.

>I want to study this fall. I'm packing my suitcases and leaving in less than a month
You seems to be in an interesting spontaneous situation, like you suddenly decided to take a break - what happened?
>The only criteria I have is that the maths is good
>Alternatively I could go and live in a village and learn maths outside of uni.
That doesn't add up for me. Do you even plan on staying in whatever place for an extended period of time? Before you go to a random village, go to a city where there is a university and the lectures are always free to visit/public like in Vienna. That's what Hitler did btw.

>>7459750
couchsurfing.com
is a website where you can write people from any city and ask if you can sleep in their places instead of a hotel. Apart from it being free then, you get to know students who will show you their university and so on. Response rate is 25 to 1 or so, so you'll have to write a bunch of people. Even if they don't have a bed, you can often just meet them. Pic related is the Max Planck institute in Göttingen, I got invited to the Christmas party in 2013 by contacting a PhD student there.
As a matter of fact, I wrote a detailed traveling report on Göttingen. It's a student city, rumor has it one quarter of people living there are students or associated with the university in some way. Infinite bikes. It has an old Innenstadt (most cities in Germany were bombed to the ground.) The girl who's appartment I crashed (math student too) literally gave me her keys after 30 minutes, and her bike too.