*blocks your path integral*

*blocks your path integral*

*goes around singularity and uses residue theorem instead*

>doesn't know what a path integral is

*unblocks your path back to *

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*

enlighten me, user.

*generalizes your theory*

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.

that's a pretty useless explanation tbqh

I'm glad that Witten memes are a thing now desu

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.

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'.

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.

>requires you know qft

not really, there is a path integral formulation for non relativistic qm, right?

Somebody got the homotopy theory copypasta screenshot with the crying number theorist?

>define
I gave the wrong the action. I meant [math]S\left[ \varphi \right] = \int {{{\left| {d\varphi } \right|}^2}} [/math]

Yes. The above action for the explicit example, is the action for just a free particle.

how bout u measure this wiener

Why does this board exist? It's Reddit tier.

It is of measure 0.

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.

I meant /r/srs/.

>no rigorous mathematical formulation

my dick may have measure 0 but at least it's dense

desu its the closest thing to old /b/ left, /b/ today is just high school trash and r9k is, well, r9k

In general there isn't. For specific theories, there are.

*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]*

>I have learned something about quantum field theories, but didn't really understand anything, so I will spout vague explanations that make me appear smart.
Explain the concepts not the mathematic tricks used to solve problems in the framework.

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)?

>vague explanations
The general definition of the path integral is vague.

Why are all smart people jewish :(

*divides by zero*

he kind of looks like doge

...

Grothendieck was born inBerlintoanarchistparents. His father,Alexander "Sascha" Schapiro(also known as Alexander Tanaroff), hadHassidicroots

We'll it depend on what you mean by "path Integral"

>This guy blocks your path integral and slaps your gf's butt. What do you do?

In the context of Witten, it is fairly obvious.

...

*Destroys mathematics*

You're in the wrong neighbourhood, experimentalist