/sci/ - Science & Math

[Anonymous No.8774873]

*blocks your path integral*

[Anonymous No.8774877]

*goes around singularity and uses residue theorem instead*

[Anonymous No.8774888]

>>8774877
>doesn't know what a path integral is

[Anonymous No.8774896]

>>8774873
*unblocks your path back to >>>/s4s/ *

[Anonymous No.8774899]

I wonder if he's given up on string theory by now. Anyone know?

[Anonymous No.8774923]

*wipes residue from his pole*

[Anonymous No.8774927]

*knocks alphabet soup out of your hand*

[Anonymous No.8775066]

>>8774888
enlighten me, anon.

[Anonymous No.8775077]

*generalizes your theory*

[Anonymous No.8775087]

>>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.

[Anonymous No.8775091]

>>8775087

that's a pretty useless explanation tbqh

[Anonymous No.8775099]

>>8774873
I'm glad that Witten memes are a thing now desu

[Anonymous No.8775103]

>>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.

[Anonymous No.8775112]

>>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'.

[Anonymous No.8775135]

>>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.

[Anonymous No.8775189]

>>8775135

>requires you know qft

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

[Anonymous No.8775212]

>>8775077
Somebody got the homotopy theory copypasta screenshot with the crying number theorist?

[Anonymous No.8775309]

>>8775103
>define
I gave the wrong the action. I meant [math]S\left[ \varphi \right] = \int {{{\left| {d\varphi } \right|}^2}} [/math]

>>8775189
Yes. The above action for the explicit example, is the action for just a free particle.

[Anonymous No.8775337]

>>8775103
how bout u measure this wiener

[Anonymous No.8775349]

>>8774896
Why does this board exist? It's Reddit tier.

[Anonymous No.8775529]

>>8775337
It is of measure 0.

[Anonymous No.8775730]

>>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.

[Anonymous No.8775732]

>>8775730
I meant /r/srs/.

[Anonymous No.8775768]

>>8775135
>no rigorous mathematical formulation

[Anonymous No.8775773]

>>8775529
my dick may have measure 0 but at least it's dense

[Anonymous No.8775775]

>>8775349
desu its the closest thing to old /b/ left, /b/ today is just high school trash and r9k is, well, r9k

[Anonymous No.8775798]

>>8775768
In general there isn't. For specific theories, there are.

[Anonymous No.8776332]

>>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]*

[Anonymous No.8776966]

>>8775087
>>8775103
>>8775135
>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.

[Anonymous No.8776988]

>>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)?

[Anonymous No.8777315]

>>8776966
>vague explanations
The general definition of the path integral is vague.

[Anonymous No.8777508]

Why are all smart people jewish :(

[Anonymous No.8777589]

>>8774873

*divides by zero*

[Anonymous No.8777794]

>>8774927
he kind of looks like doge

[Anonymous No.8777938]

>>8777508
>>8775077

[Anonymous No.8777951]

>>8777938
Grothendieck was born inBerlintoanarchistparents. His father,Alexander "Sascha" Schapiro(also known as Alexander Tanaroff), hadHassidicroots

[Anonymous No.8778590]

>>8774888
>>8774877
We'll it depend on what you mean by "path Integral"

[Anonymous No.8778606]

>>8774873
>This guy blocks your path integral and slaps your gf's butt. What do you do?

[Anonymous No.8778607]

>>8778590
In the context of Witten, it is fairly obvious.

[Anonymous No.8778661]

[Anonymous No.8778871]

*Destroys mathematics*

[Anonymous No.8779264]

You're in the wrong neighbourhood, experimentalist