The previous one () is about to reach the bumplimit, so let's start a new one.
>what are you researching?
>what are you studying?
>any good problems?
>book recommendations?
>cool theorems?
Math General
Luke Jenkins
Other urls found in this thread:
freebookcentre.net
Veeky
arxiv.org
twitter.com
Ryan Wright
first fro ct
Dominic Myers
freebookcentre.net
This is the best collection of free online texts I've seen. Has texts on pretty much every subject of mathematics except logic and a few specific sub fields.
Julian Moore
general advice for an undergrad math major?
Lucas Ward
about mathematics itself or academics/careers?
Brody Gomez
>what are you studying?
Renormalization techniques for TQFT.
One of the defining features of a TQFT is the functoriality [math]\tau(M) = k \tau(M_1)\circ f_{\#} \circ \tau(M_2)[/math] where [math]k\in K[/math] is an invertible element of the ground ring, and [math]M[/math] is a [math]\mathscr{B}[/math]-space glued together from two cobordisms [math]M_{1,2}[/math] along the [math]\mathscr{A}[/math]-homeomorphism [math]f: \partial_+ M_1 \rightarrow \partial_- M_2[/math]. A TQFT is said to be anomaly-free if [math]k = \operatorname{id}_K[/math].
Apparently the existence of a [math]G[/math]-valued 2-cocycle [math]g \in \mathscr{P} \otimes G[/math], where [math]\mathscr{P} = \{P = (M,N,f) \mid M, N \in \mathscr{B}, f: \partial_+M \rightarrow \partial_- N\}[/math] is the collection of gluing patterns [math]P[/math] between [math]\mathscr{B}[/math]-spaces, on the cobordism theory [math](\mathscr{B},\mathscr{A})[/math]is sufficient to guarantee that the TQFT [math](\mathscr{T},\tau)[/math] based on it (possibly with anomalies) can be made anomaly-free.
This is a generalization of the usual process of renormalization in QFT where the quantum anomalies are gauged away by gauge-fixing in gauge-space (say that three times fast). The [math]k[/math] can be thought of as an obstruction to the quantum Ward identities.
Ethan Garcia
99.7% sure the majority of uses of renormalization are not cases where you can sharp ans sweet get rid of particularly well specified QFT anomalies
Jose Nguyen
Your overly verbose posts are genuinely cringe-inducing. Especially since what you keep yammering on about is (non-deep) category theory and elementary topology thinly veiled in pretentious physics lingo.
John Baker
And those would correspond to cases where you can't find the 2-cocycle.
Remember that TQFTs only contains topological data. Normal QFTs also contains dynamical data that needs to be taken into account when renormalizing. This is part of the reason why non-renormalizability is rampant in QFTs with non-Abelian interactions or non-conformal geometry.
Nicholas Martin
some resources for computer science math for beginner?