/sci/ - Science & Math

>>11335316
>gravity consistent with GR

>>9300339
Let [math](M,\omega)[/math] be a symplectic [math]SO(3)[/math]-manifold admitting a complete Hamiltonian [math]G[/math]-action [math]a:\mathfrak{g} \rightarrow \Xi(M)[/math], a particle with spin is then described by a trajectory [math]q:\mathbb{R}
\rightarrow M[/math] such that [math]q[/math] minimizes the action function [math]S(q,\dot{q})[/math] of a Hamiltonian [math]H\in C^\infty(M)[/math] and whose polarization is invariant with respect to the coadjoint action of [math]G = SU(2)[/math]. From this and the fact that [math]SO(3)[/math]-bundles are [math]SU(2)[/math] equivariantly formal, the Chern-Weil homomorphism [math](S\mathfrak{g}^*)^{SO(3)} \rightarrow \Omega_{SU(2))}(SU(2)/SO(3))[/math] on the equivariant cohomology induces an isomorphism [math](S\mathfrak{g}^*)^{SO(3)} \cong H_{SU(2)}(SU(2)/SO(3)) [/math]. This gives rise, for each [math]SO(3)[/math]-invariant element of [math]\mathfrak{so}(3)^*\cong \mathfrak{su}(2)^*[/math], to a symplectic form [math]\omega_{SO(3)}[/math] on the coadjoint orbit of [math]SU(2)/SO(3)[/math], and how this symplectic form transforms under symplectic diffeomorphisms determines the spin of the particle [math]q[/math] with polarization in a connected component of the quotient [math]SU(2)/SO(3)[/math].
Hopefully this clears up any confusion.

>>8457119

Go on buddy, tell us the difference. I'll wait.

i would suggest that 3 does not equal 3, as both instances of the number 3 are not the same instance.

>Is happy
>Has to flaunt his happiness to people he perceives to be less happy
I always love it when these sorts of posts show up on 4chan.

I'll just copypasta a few things /jp/:

http://en.wikipedia.org/wiki/Hedonic_treadmill
http://en.wikipedia.org/wiki/Downregulation_and_upregulation
http://www.ted.com/talks/dan_gilbert_asks_why_are_we_happy.html
http://en.wikipedia.org/wiki/Drug_tolerance


You're basically pre-programmed by biology to have a fixed hapiness level, even if absurdly bad or absurdly good things happen to you.

Lottery winners

Amputees

These people experience sudden influxes of happiness or un-happiness one way

Within several months to a year, they rate themselves as hardly any more or less happy than they were before their big event happened.

You can be a NEET, and it might be really fun for a while, but reality is that you can't be happy all the time forever. It goes for drug addicts, people on binge on anything really.

All you can do is try to live a LONGER life. And try to aim to feel satisfied when it's over.

It that's NEETism, so be it. I would think NEETism, if you have enough funds, is pretty great. Most people call this "early retirement"

The thing is they expereince a LOT OF VARIED THINGS! when not working

If you binge on anime and vidya and whatever, you'll lose whatever pleasure you got from it.