/sci/ - Science & Math

>>10235166
>what are the requirements for representation theory
Group theory, linear algebra, characters.
>Von Neumann algebras
Group/ring theory, modules, Lie theory, functional analysis.
>geometric quantization
Symplectic geometry, differential geometry/topology, classical Lagrangian mechanics.

>>10111235
>should I go for functional analysis or linear analysis first?
What do you mean by "linear analysis"? Harmonic/wavelets?

>>9842089
>There are many parameters in the way tho.
You should've figured this out through doing undergrad research, if you were in NA at least.
Abilities aside you should be doing what you find the most interesting, because frankly speaking there is very little intersection between nonperturbative QFT (a la Strocchi, Swieca, etc. which mainly deals with regularity of the theory) and string theory (a la Witten, Moore, etc. which mainly deals with the algebra of the theory), which means that you really have to pick one and only one between them if you want to contribute something substantial.

https://arxiv.org/abs/1604.06527
>This produces a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group.
>>9571617
>is it bad that my uni specializes in something
No.
>>9571680
>particle pairs
Formation of for instance Cooper pairs is a physical fact, not a mathematical one. Though there are mathematical ways of classifying if a particle pairing can give you an exactly solvable system or not.
Tinkham has a good introduction to BSC superconductivity via Cooper/Peierls pairs.
>local and global broken symmetry
Vector bundles. Specifically principal complex/Hermitian [math]G[/math]-bundles. Gauge transformations arises naturally in this setting as fibre-preserving endomorphisms of the universal bundle.
>spooky motion
There's no such thing.
>>9572738
>No idea where to start.
It should be your advisor's job to tell you that.
>>9572790
Miles Mathis is a famous crank my dude.
>>9572858
>I understand they are not the same thing in many way
They are, and they should be treated as such. Theorists that do not value and maintain at least some level of rigor are nothing more than experimentalists.
>>9573608
Use Weinberg for QFT and supplement with Streater-Wightman.
Also renormalization by the cancellation of counterterms is a physical procedure, not a mathematical one. You being a mathematician or not has nothing to do with it, because there is no mathematical justification for why we do it, just why and how it works.

>>9532957
>My only point is that for each field configuration, there exists a state in the Hilbert space corresponding to that field configuration.
This is not strictly true, and neither is the converse. The asymptotic states [math]\Psi_\text{in/out}[/math] may not have a [math]L^2[/math] representation and an instanton (a single quantum state) gives rise to a number of distinct field configurations equal to the topological charge of the model. The former leads to the divergence of the S-matrix and is an independent problem. The asymptotic completeness axiom can sweep this problem under the rug but its consistency with the rest of the Wightman/Osterwalder-Schrarer axioms is still tenuous at best.

>>9396363
Right and wrong. Physicists of the older generation are more likely to reject fancy mathematical constructs, but I'm sure this is about to change.
see Fujikawa - Path Integrals and Quantum Anomalies

>>9317124
Yeah. I did that one years ago.