"Ahogy Witten írta valahol, az emberek nem ismerik a fizika ezen mélységeit, mert a többség nem tanulta."
"Electromagnetism can be described by U(1) gauge theory, as undergraduates are taught, though not always in precisely that language. According to the StandardModel, a more complete description of nature, including the weak interactions as well as electromagnetism, can be obtained by starting with a gauge group that is U(2) (or SU(2)×U(1)); the global structure will not be very important in our discussion and depends on considerations that we will omit, such as the existence of quarks).If U(2) gauge theory is a better approximation to nature than U(1) gauge theory,why is it that undergraduates learn about U(1)? The answer to this is gauge symmetry breaking. For largely unknown reasons, it is energetically favored fora phenomenon to occur that effectively reduces the structure group from U(2) to U(1). Physically, this means that most observations at distances and times that are large compared to the nuclear scale can be adequately described byU(1) gaugetheory."
Ez a kedvencem. Ugyan le volt már írva a fermion wikin, de mindig jó olvasni.
"The most interesting property of the SG model is the existence of classical, stable solutions of the equations of motion – solitons and anti–solitons [1]. Solitons can annihilate with anti–solitons. Many–soliton solutions obey Pauli’s exclusion principle. As pointedout by Skyrme [4] this can be interpreted as a fermion–like behaviour"
"From a modern point of view, the vector potential is a connection, which we will call A, on a unitary complex line bundle L.F is interpreted as the curvature of the connection; thus if A is represented locally as a one-form, we have F=dA"
A jelölésekre nagyon kell figyelni. Többek közt nem mindegy, hogy az einsteini összegzésnél a jelölés alul van vagy felül.
Itt pl az egyenletben két "A" van látszólag. Csakhogy a két "A" kissé eltérő.
Én a bal oldaliról írtam, ez az elektromágnesesség terének vektora. Az egyenlet jobb oldalán a weak isospin jelöli az "A". Ezt legtöbbszőr W-vel jelölik. (nem értem, miért kell valamit össze-vissza jelölni. És ezt néha még Witten is megteszi, Unatkoztok vagy mi?)
A kis "b" a weak hypercharge jele, ami általában "B".
Honnan lehet tudni azt, hogy a weak hypercharge és a weak isospinhez rendelhető bozon is vektorbozon?
Nos ismerni kell a jelöléseket. Az A(Mű) nem más, mint az elektromágnesességhez tartozó négyes vektor potenciál. Szóval a többi vektor is négy dimenziós, hiszen megkapják ugyan azt az indexet.
The AdS/CFT correspondence is often described as a "holographic duality" because this relationship between the two theories is similar to the relationship between a three-dimensional object and its image as a hologram
"The duality represents a major advance in our understanding of string theory and quantum gravity.[1] This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle,"
"The other paper calculates the internal energy of the corresponding lower-dimensional cosmos with no gravity."
"While anti-de Sitter space does not correspond to gravity in general relativity with the observed cosmological constant, an anti-de Sitter space is believed to correspond to other forces in quantum mechanics (like electromagnetism, the weak nuclear force and the strong nuclear force). This is called the AdS/CFT correspondence."
"By applying the AdS/CFT correspondence, Sơn and his collaborators were able to describe the quark gluon plasma in terms of black holes in five-dimensional spacetime. "
". Some condensed matter theorists including Subir Sachdev hope that the AdS/CFT correspondence will make it possible to describe these systems in the language of string theory and learn more about their behavior."
"More precisely, their results apply to black holes that are approximated by extremalKerr black holes, which have the largest possible angular momentum compatible with a given mass.[77]They showed that such black holes have an equivalent description in terms of conformal field theory. The Kerr/CFT correspondence was later extended to black holes with lower angular momentum.["
Ahogy Witten írta valahol, az emberek nem ismerik a fizika ezen mélységeit, mert a többség nem tanulta.
Azért nem tanítják ezt, mert igazából erre senkinek sincs szüksége.
Nem kell azt tudni, hogy a foton-mező, avagy az elektromágneses mező igazából két mező keveredéséből jött létre, hiszen ez a két mező önmagában már nem létezik. A Higgs "kifagyása" végérvényesen összeláncolta a B0 és a W0 bozon-mezőt. (weak hypercharge és a weak isospin amiről beszélek). Az elektromos töltés a hipertöltés és a gyenge izospin harmadik komponenséből adódik ki.
Szóval igazad van, ( de az egész nem ilyen egyszerű )
Ez annyit mond, hogy pl az elektromos tér függ a vektorpotenciál idő szerinti deriváltjától és a skalár potenciál gradiensétől (ami szintén első derivált csak nem idő szerinti). Magyarul akkor van elektromos tér, ha a vektor mezőben változás van. Egy "uniform" vektrokmező láthatatlan számunkra. Se elektromos se mágneses teret nem fogunk benne mérni.
És most jön be Skyrme elmélete, mi van akkor, ha az elektron ( és majd később minden fermion ) valójában csak egy topológiai "csavatodás" (twist) valamilyen (pl elektromágneses) vektormezőben?
Csak ott fogunk elektromos (és mágneses) teret tapasztalni, ahogy ez a vektormező csavarodik...
Megfeleltethető-e a gravitáció egyfajta folyadék áramlásnak?
Igen ha a térbeli dimenzió eggyel csökken.
we will study a particular long wavelength limit of Einstein’s equations with a negative cosmological constant in d + 1 dimensions. In such a limit we find that Einstein’s equations reduce to the equations of fluid dynamics (relativistic generalizations of the famous Navier-Stokes equations) in d dimensions. https://arxiv.org/pdf/1107.5780.pdf
Solitons https://www.stringwiki.org/wiki/Solitons These vortices arising in the theory with extra flavors are related to other solitons,known as a sigma-model lumps. (These solitons have other names, depending on thecontext, sometimes referred to as ”textures”, ”Skyrmions”or, in the context of stringtheory, worldsheet instantons”). TASI Lectures on Solitons Instantons, Monopoles, Vortices and Kinks David Tong , Cambridge https://arxiv.org/pdf/hep-th/0509216.pdf https://www.youtube.com/watch?v=zNVQfWC_evg These lectures cover aspects of solitons with focus on appli cations to the quantum dynamics of supersymmetric gauge theories and string theory. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid state physics, as well as having ties to certain areas of string theory. https://en.wikipedia.org/wiki/Skyrmion https://en.wikipedia.org/wiki/Pion This model admits topological solitons called Skyrmions. https://en.wikipedia.org/wiki/Chiral_model https://en.wikipedia.org/wiki/Sine-Gordon_equation Quantum version: The exact quantum scattering matrix was discovered by Alexander Zamolodchikov. This model is S-dual to the Thirring model. The Thirring model is an exactly solvable quantum field theory which describes the self-interactions of a Dirac field in (1+1) dimensions. https://en.wikipedia.org/wiki/Thirring_model
In a quantum field theory, there can be field configurations of bosons which are topologically twisted. These are coherent states (or solitons) which behave like a particle, and they can be fermionic even if all the constituent particles are bosons. This was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named skyrmions after him. https://en.wikipedia.org/wiki/Fermion#Skyrmions The analogy between the Skyrme field and the Higgs field of the electroweak sector has been used[4] to postulate that all fermions are skyrmions. This could explain why all known fermions have baryon or lepton quantum numbers and provide a physical mechanism for the Pauli exclusion principle.
12.4. Skyrme suggested that nucleons are solitons of pions. 12.5.Solitons of bosonic fields can have half integer spin and be fermions. This is because of very subtle topological facts. When an infinite number of particles act in unison, the usual rules of quantum mechanics can be overcome http://www.pas.rochester.edu/~rajeev/phy581/S10ParticleLect.pdf
An important example are the solitary waves of the ocean: tsunamis. Pions are like the more familiar ripples on the surface of the oceans. These cost very little energy. But given a lot of energy (in the case of ocean wave it is provided by an earth quake) we can also create a huge new wave that looks like an entirely new particle. Skyrme suggested that nucleons are just such solitons of the pion field. At the time this idea was suggested (1960s) it was ignored because it was just too bizarre. But about mid eighties a group of us revived it and showed how it is in fact another way to look at QCD. Although QCD itself is too difficult to solve, in simpler cases where it is possible to solve gauge theories, we have shown that nucleons indeed are solitons. https://arxiv.org/pdf/hep-th/0010225.pdf https://arxiv.org/pdf/hep-th/9412184.pdf
