/sci/ - Science & Math

>>11527907
>Quevedo
https://arxiv.org/abs/0712.0868
Good stuff.

>>11334824
You need a globally-defined top-degree form, or a section of the normal bundle, that does not change sign for orientability. The Mobius strip isn't orientable because locally defined normal vectors must invert as you move (in a loop) once around the Mobius strip.
>>11334854
Try putting [math]x = \sin\theta[/math] in the first function and [math]x=\tan\theta[/math] in the second.

>>11186389
I can vouch for this book, Gamov is quite reputable.
>>11186375
In addition to what anon has already suggested, I also recommend Simon & Read's series on methods of mathematical physics. It delves mainly into foundations of QM and QFT in the later volumes but most of the background in Vol. 1, such as ergodic and representation theory, do see major applications in stat mech.
Besides, there's an exact mapping between [math]d[/math]-dimensional QFTs and [math](d+1)[/math]-dimensional stat mech systems.

>>10385612
Wen and Nakahara.

>>10358911
Take the contractible infinite-sphere [math]S^\infty[/math] as the space of unit-norm wavefunctions [math]\psi[/math] in a Hilbert space [math]\mathcal{H}[/math], then chiral symmetry [math]\Gamma \psi = -\psi[/math] identifies diametrically-opposite wavefunctions such that the physical Hilbert space [math]\mathcal{H}_\text{phys} = S^\infty/\mathbb{Z}^2 = \mathbb{C}P^\infty[/math] is exactly the infinite-dimensional complex projective space [math]\mathbb{C}P^\infty[/math], where [math]\mathbb{Z}_2 = \{1,\Gamma\}[/math] is the chiral symmetry groud.

>>10215669
I've taught my cat how to do RG analysis, integration should be easy.

>>10178751
Colour is from [math]SU(2)[/math] weak nuclear forces, flavour is from [math]SU(3)[/math] strong nuclear forces. There are 3 generators (the Pauli matrices) of the Lie algebra of [math]SU(2)[/math] which correspond to the 3 colours, while there are 8 generators (the Gell Mann matrices) of the Lie algebra of [math]SU(3)[/math] which form the 8 flavours.
By adding [math]U(1)[/math] EM gauge group to weak [math]SU(2)[/math] gauge group, we get the full [math]U(2)[/math] gauge symmetry under which the colours can be assigned "charges", i.e. Lorentz-invarnat spinor representations of [math]U(2)[/math]. This can be done because [math]U(2)[/math] is a 4-dimensional Lie group and hence admits a spinor structure. You CANNOT do this non-trivially (namely there are no spinors with non-trivial "flavour charges", whatever that may mean) with [math]SU(3)\times U(1)[/math], as its Lie algebra is a 9-dimensional manifold on which no spinor structure exists.
It'd be good to read a book first before posting, my keen undergrad friend.

>>10160056
Frankel for math Nakahara for physics.

>>10119112
Cobordism/tangle hypothesis and Witten conjecture. Just for fun I'll throw in the 5/2 Quantum Hall state.

>>10057243
The magnetic flux threading through the plane manifests as the puncture since no particle can access its core due to its Lorentz force. In addition, the symplectic potential I gave is exactly the Landau gauge for the magnetic field. You would've known this if you did even the tiniest bit of research; all of this very basic stuff is covered in Wen and Auerbach.
You should've use the 3 brain cells left in your head first before posting, dear.

>>9842757
>I thought you were the guy who was at the same uni as him
I did do my masters at the same uni, but I never really had a chance to talk to him back then and have even less chance now. Never took a course from him either.
I've been to some of his concerts though, they're pretty good.

>>9395397
>using incorrect intuition to understand something yields "spooky" results
Wow who would've thunk??

>>9354105
Kronecker.
>Why is it N, shouldnt it be 0 since all term would cancel each other ?
What?

>>9349683
study now

>>9340482
>What do very smart physicists pursue today?
Conformal field theory
Topological quantum field theory
Geometric quantization
Quantum algebra
Quantum integrability
Singularity theory
Twistor theory
tt* geometry
Mirror symmetry