/sci/ - Science & Math

>>9441154
I sure hope Scholze wins instead of some token black arab tranny.

>>9412193
Visualize an n-space and set n = 4.

>>8782825
Fuck I misread your post sorry.
>What happens if [math]T_{\mu\nu} \neq \frac{\delta W[A]}{\delta g^{\mu\nu}}[/math] ?
That's the definition for the energy-momentum tensor. You can consider [math]g^{\mu\nu}[/math] as a general infinitesimal coordinate transform.
>>8782851
Wait so I actually didn't misread your post?
The reason it's bad is because physical quantities are meant to be gauge invariant as well as independent of any arbitrary mathematical choices of how you look at the quantity. You can think of this as like changing coordinate systems in classical mechanics, which should not alter the equations of motion and hence the particle trajectories of the system.
The reason that we don't want the quantum action to depend on the compactification radius is similar. Changes in the compactification radius correspond to a conformal transformation, and for CFTs physical quantities like the partition function and the quantum action are required to be conformally invariant.

>>7754295
You need a volume density. Use [math]\rho(x,y,z)=\delta(y)\delta(z)\left(\theta(x-a)-\theta(b-x)\right)[/math] and integrate
[math]V = \int_{\mathbb{R}^3}d^{3}x\rho(x,y,z)[/math]
>inb4 physicist detected