/sci/ - Science & Math

[Anonymous No.11004706]

>relativistic qfts are still not analytically well defined
>not even ontologically well defined
>not well defined in essentially any sense

this makes learning field theory very frustrating if you're trying to avoid retarded 'quantization' heuristics.

[Anonymous No.11004713]

>>11004706
I read that as relativistic qts and now I'm sitting her yearning for a qt lab partner physicist gf to keep my lab coat warm.

[Anonymous No.11004724]

>>11004706
except they make definite predictions, and the predictions are correct. it’s been coded up, check out MadGraph or Pythia or FeynRules. not to mention Geant or the slews of other generators like sherpa or herwig

[Anonymous No.11004738]

>>11004724
Oh sure, nobody has any issues with the perturbative work, but when you start poking around the ideas surrounding or "leading" up to the feynman rules, lsz, et cetera, you find them pretty conspicuously lacking, It is as if there is a well worn trail taking you up to your destination, but if you wander a few meters off the trail you find yourself mired in a swamp of spurious ideas.

[Anonymous No.11004919]

Your first statement is false, OP. Many QFTs in 2 and 3 dimensions have been rigorously established, Unitary CFTs for instance are very well understood. The standard model has not, and Yang Mills theory has not, but these are outstanding cases of a more general picture of what constitutes a quantum field theory.

>QFT is feynman rules
This is likely the source of your confusion

[Anonymous No.11004925]

Local Quantum Physics: Fields, Particles, Algebras - Rudolf Haag

Read this and tell me a local relativistic quantum field theory is not a well-defined concept.

[Anonymous No.11004936]

>>11004706
>magnets are not well defined
>lol the field just exists bro
>it's lines and stuff, curves in space
>here, look at this differential equation

[Anonymous No.11004945]

They are defined in the context of physics, which is all that matters for a physicist. Why call them heuristic rules if they are perfectly tractable and give you enough methods to describe a fuckton of quantum phenomena? Would you call Newton's principia a bunch of ill defined heuristics because the framework was not developed rigorously until much latter?

[Anonymous No.11004992]

>>11004706
We very much know how it [math]should[/math] be defined. In fact, free relativistic QFTs a la Haag-Kastler are mathematically well-defined in terms of local nets of observables and representation theory thereof, or via Baez-Zhang in terms of symplectic nets of probability measures.
The entire problem is with scattering, in which particle interactions may lead to no amplitudes satisfying both the required physical (e.g. crossing symmetry) and mathematical (e.g. analyticity/meromorphicity) conditions.
There are several classes of mathematically well-defined interacting relativistic QFTs, however:
1. QFTs with fields satisfying the Strocchi-Swieca conditions, which have well-defined [math]S[/math]-matrices,
2. QFTs reconstructed from an interacting Euclidean FT, whose amplitudes have relaxed analytic conditions and the relativistic versions can be Wick rotated,
3. QFTs whose (quantum) dynamics can be described by SDEs, and whose renormalization can be captured via recently developed "regularity structures" of Hairer, or
4. QFTs obtained on hyperkahler manifolds that admit a Kostant-Souriau quantization of the jet bundle.
Not to mention relativistic QFTs with mostly topological/geometric data (i.e. very little dynamics), such as TQFTs and CFTs, can be mathematically defined, written down and classified completely categorically. This line of thinking has recently been pushed to study superconformals, SuGras and (SUSY) strings and sees application in homological mirror symmetry and even geometric Langlands.
Even standard texts like Weinberg covers some of the required foundations such as Dirac's quantization of classical holonomic constraints. So no, the problem is with you, not with relativistic QFT.

[Anonymous No.11005012]

>>11004992
good post

[Anonymous No.11005042]

>>11004713