*It's fun to stay @ the YITP
This paper is quite long, so here we present just the Abstract:
The Cubical Cow
Physics generally uses approximations, because the math is too hard. A standard one is the sphere, because of symmetry, but this causes close-packing problems, as well known in the shipping industry, poultry farming, and agriculture [1,2].
For this reason, we propose instead to use (hyper)cubes. This also has the huge advantage of favoring Cartesian coordinates over spherical, the latter requiring trigonometry that nobody remembers beyond 2 dimensions. And we can expand in just plane waves, instead of those awful spherical harmonics. Furthermore, no topological complications are introduced by this change.
A familiar, standard example is the cow. (Technically, this is sexist terminology, and "cattle" or "ox" should be used instead. But we will udderly ignore such politics.) Replacing spheres with cubes resolves such problems as the inconsistency of spherical digestive tracts, which is closely related to the nonexistence of spherically symmetric magnetic fields. (I.e., digestive tracts must have both a positive & a negative "pole".)
Cubical Field Theory
In the original concept of atoms by the famous ancient Greek philosopher Particles (Παρτικλῆς), the fundamental constituents of everything were assumed to come in various shapes & sizes. Even though more modern terminology calls them "points", the existence of the classical electron radius & Compton wavelength shows they have extent. Although quantum mechanically they are also waves, a simpler apprcowimation is to treat them as square waves rather than round ones. The arguments for their roundness were in any case handwaving (or handparticling, in particlar).
An example of the use of non-round particles is hedronism: the use of amplituhydra, such as the rhododendron, in hedronic physics. This has become one of the dominant approaches to CFT.
Interactions of hedrons is most simply calculated with laptons [💻].
Unfortunately, the IR divergences cannot be regularized without destroying conformal invariance, so it's hard to see the forest for the loops.
(Such problems do not yet appear in the Boring approximation.)
As is well known [🤨], the simplest interaction terms in quantum field theory are cubical. (In fact, spherical terms are never considered.)
We first analyzed path integrals as ordinary integrals in dimension D = 0.
Canonical quantization wasn't applicable, since it's a waste of time, & there is no time in D = 0.
Then ∀D we calculated tree-level scattering (including Chuck Taylor amplitudes) all the way up to 12pt, but not higher because the fontsize would be too large.
This is sufficient to analyze amplitudes @ NNNNNNNNLOL.
For loop amplitudes, we used the following approximations:
1/N expansion: 3 ≫ 1
asymptotic safety: 2 ≪ 1
In particular, we evaluated all multiloop tadpoles, which can be expressed in terms of polywogarithms.
Idiocy of Tea
A popular example in high-energy theoretical physics is the Idiocy of Tea correspondence, where fields in the bulk are related to those on the boundary using the Legendry transform. Here flat 10D spacetime is replaced by the product of a 5D sphere with a Wick rotation of the 5D sphere.
Using Eddington's theory of General Relativity (based on earlier work by Einstein), we can calculate propagators on AdS space, but they are too messy to use in practice. And the superstring action is practically impossible to quantize on this background, so the path integral becomes Guessian.
As a result, people have resorted to using progressively cruder aprcowimations to produce results. For example,
AdS5 → AdS4 → AdS3 → AdS2 → AdS1 → AdS0
CFT4 → CFT3 → CFT2 → CFT1 → CFT0 → CFT-1
superstring → supergravity → metric → scalars
particle physics → nucular physics → condensed metaphysics → cosmology
or in other words,
big dimensions → small
big fields → small
high energy → low
There has been a corresponding reduction in the number of results.
This work was supported by an n.s.f. grant & an NSFW grant.
These topics were already treated in previous papers [🤓], but are updated here.
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