*blocks your path integral*
*goes around singularity and uses residue theorem instead*
>>8774877
>doesn't know what a path integral is
I wonder if he's given up on string theory by now. Anyone know?
*wipes residue from his pole*
*knocks alphabet soup out of your hand*
>>8774888
enlighten me, anon.
*generalizes your theory*
>>8775066
Something of the form [math]\int {{\cal D}\varphi } \exp \left( { - S\left[ \varphi \right]} \right) [/math]. Definition of the measure dependent upon the definition of the action S.
>>8775087
that's a pretty useless explanation tbqh
>>8774873
I'm glad that Witten memes are a thing now desu
>>8775091
Physically it is used to define a quantum theory by defining correlations:
[math]\left\langle {\varphi \left( {{x_1}} \right)\varphi \left( {{x_2}} \right)} \right\rangle = \frac{{\int {{\cal D}\varphi } \exp \left( { - S\left[ \varphi \right]} \right)\varphi \left( {{x_1}} \right)\varphi \left( {{x_2}} \right)}}{{\int {{\cal D}\varphi } \exp \left( { - S\left[ \varphi \right]} \right)}}[/math]
To give an explicit mathematical example. Take phi as a parameterized path and define [math]S\left[ \varphi \right] = \int {d\varphi } [/math]. Then the measure [math]{\cal D}\varphi [/math] can just be given as a Wiener measure.
>>8775103
this is not a good explaination either, it is not sufficiently physical nor is it sufficiently general in a mathematical sense as to describe 'functional integration'.
>>8775112
A full physical explanation requires you to know QFT. There is no rigorous mathematical formulation in general.
As I said, definition of the measure (i.e. the rigorous part) depends upon what your action is. Action depending upon the specific physical theory.
>>8775135
>requires you know qft
not really, there is a path integral formulation for non relativistic qm, right?
>>8775077
Somebody got the homotopy theory copypasta screenshot with the crying number theorist?
>>8775103
how bout u measure this wiener
>>8774896
Why does this board exist? It's Reddit tier.
>>8775337
It is of measure 0.
>>8775349
Are you serious? /s4s/ was made as an april fools joke, parodying /srs/ with trigger warnings and shit like that. The people on the board liked it so they never got rid of it.
>>8775730
I meant /r/srs/.
>>8775135
>no rigorous mathematical formulation
>>8775529
my dick may have measure 0 but at least it's dense
>>8775349
desu its the closest thing to old /b/ left, /b/ today is just high school trash and r9k is, well, r9k
>>8775768
In general there isn't. For specific theories, there are.
>>8774873
*defines Mauer-Cartan form [math]\mu = X^{-1}dX[/math] and constructs the WZW action [math]S_{WZW}(f) = \frac{k}{8\pi^2} \int_{D}\operatorname{tr}\left(f^{*}\mu\right)^3[/math]*
>>8776966
Do you actually want to know something or are you just aggressive because you feel like it?
Do you know the path integral formulation for quantum mechanics (not fields in R^4)?
>>8776966
>vague explanations
The general definition of the path integral is vague.
Why are all smart people jewish :(
>>8774873
*divides by zero*
>>8774927
he kind of looks like doge
>>8777938
Grothendieck was born inBerlintoanarchistparents. His father,Alexander "Sascha" Schapiro(also known as Alexander Tanaroff), hadHassidicroots
>>8774873
>This guy blocks your path integral and slaps your gf's butt. What do you do?
>>8778590
In the context of Witten, it is fairly obvious.
*Destroys mathematics*
You're in the wrong neighbourhood, experimentalist