User:Likebox/WikiProjectPhysics Some Needed Mathematical Content

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The following mathematical artices are needed, in no particular order:


 * 1) Anything on Scholarpedia.
 * 2) S matrix theory--- This subject requires detailed presentation, although much of it is of historical interest only.
 * 3) Condensed matter RG--- the RG pages need expansion from Domb and Green. Wilson Fisher point, O(N) models and the like.
 * 4) Nonstandard string vacua--- there aren't only 5 string theories: Hellerman discovered a 6th 10d theory with SUSY, and there were O(16)xO(16) heterotic strings with no SUSY, and a bunch of other constructions.
 * 5) Representation theory for physics: SU(N),SO(N),Sp(N),exceptional each need an article, and all the popular reps and breakdown, plus Clebsch-Gordon need summarizing in articles. I prefer Weyl method here.
 * 6) Kac Moody Lie Algebras--- The physics version.
 * 7) Conformal field theory--- Belavin Polyakov Zamoldchikov and the rest--- huge field is barely covered.
 * 8) Supersymmetry--- the mess here is the notation (you need a unified multidimensional spinor notation and I can do that, following Scherk from the 70s, avoid 2 component stuff for general formulations--- that's 4d specific).
 * 9) Knot theory/Chern Simons theory (this cross talks with math)
 * 10) Scattering theory (relativistic scattering, shadow scattering--- I alway liked Peierls "surprises in theoretical physics")
 * 11) Grassman integrals for lattice models--- dimer models/Ising determinants/etc.
 * 12) Axiomatic field theory
 * 13) PT invariant theory: Frohlich Bender etc. Recent work which needs an article.
 * 14) Unparticles: Georgi Banks/Zaks etc. Recent work which needs an article
 * 15) AdS/CFT: get a good technical review.
 * 16) AdS/CMT (Schrodinger groups) new application.
 * 17) Fermi liquid theory described as oscillations of the Fermi sphere (this is an obscure description from the 60s, but it should be more widely known, I can't remember the cite offhand)
 * 18) Petrov Classification
 * 19) Exact solutions of GR: find them all and put them in.
 * 20) Landauer style computational thermodynamics, reversible computation.
 * 21) Potts model and other 2d solvable models
 * 22) Wolfenstein mechanism (neutrino oscillations and solar model)
 * 23) Anomaly land, triangle, hexagon, Fujikawa, Green-Schwarz
 * 24) OPE--- this needs to not be a stub. Wilson and Zimmerman, but also 2d stuff.
 * 25) Chiral perturbation theory: Skyrmions and nonlinear vs linear sigma models. Need to sort out whether there is a sigma (I don't know if this is known).
 * 26) classical chaos: bifurcation theory, periodic orbits
 * 27) Quantum chaos: cat map, Heller scarring, Gutzwiller trace formula
 * 28) Unified thermodynamics statistical mechanics treatment
 * 29) Ergodicity theory in physics: billiards on a negatively curved space
 * 30) Weak localization--- applications to metal rings, perturbative calculations
 * 31) Universal conduction fluctuations
 * 32) Singularity theorems
 * 33) Membrane paradigm
 * 34) D-brane junctions
 * 35) Supersymmetry current --- the multiplet is confused
 * 36) Current algebra--- there are a ton of models here, focus on 80s-now, not 60s.
 * 37) BFKL pomeron--- Polchinski and Strassler along with Lipatov sorted this out recently, but this needs a historical treatment, it's big.
 * 38) AdS/QCD--- there are top down and bottom up models, both interesting.
 * 39) Matrix models and 2d strings--- this was semi-obscure literature in the 80s popularized by Polchinski.
 * 40) Anderson localization--- 2d used to be controversial, but it looks like the controversy is over, no localization in infinite 2d system.
 * 41) Rigorous fermi pressure theorems, stability of bulk matter (dyson etc, famous work from the 60s, obscure today)
 * 42) QED precision calculations--- high order diagrams, muon magnetic moment, proton radius corrections, etc. Kinoshita does this, and he's dead soon.
 * 43) Bethe Salpeter equation --- this is on Scholarpedia, but they have no technical presentation, so I present it separately.
 * 44) Atomic Hartree Fock theory--- this is still the best standard for atomic spectra, we need an article on the metod, the calculations for a few atoms, some variabtional stuff for He, and best results
 * 45) Nuclear drop model--- this was more than the binding energy curve, it was also fission. Someone should read Bohr on this.
 * 46) Nuclear shell model--- magic numbers/Skyrme alpha particle model
 * 47) Nuclear effective potentials--- the relation to hadronic resonances, predictions for low lying levels etc.
 * 48) Bethe Ansatz/ inverse scattering method/ Heisenberg model--- this is a field.
 * 49) spin networks, a-la penrose--- this links up with Chern Simons theory
 * 50) Canonical GR--- this is badly under represented everywhere--- everyone should have a good Ashtekar variables exposition available.
 * 51) York Hawking boundary term (not Hawking boundary term)--- this needs to be given and explaned.
 * 52) Parton physics: Feynman, Gribov, Rajeev's 2d model
 * 53) 3-d Gauge theory: Feynman Carbali-Nair
 * 54) Quantum computing: Shor Grover adiabatic algorithms
 * 55) SUSY exact solutions
 * 56) Seiberg Witten theory (physics) following 94 paper, or 97 WItten paper (the latter is better)
 * 57) Nicolai maps (everyone needs to know this, but it is persistently obscure)
 * 58) Morse theory and SUSY (Witten loves this paper of his, I don't know why, but I trust him)
 * 59) Giant magnetoresistance--- this field is no longer hot, but used to be.
 * 60) Fractional QHE (again Chern Simons, but with applications--- noncommutative geometry)
 * 61) Berry Singularities of wave equations (this was a nice talk I saw by him)
 * 62) Viscous fluid flows in 2-d capilaries (Feigenbaum did some wonderful work here)
 * 63) Robust Differential Equation models (these are becoming annoyingly prominent in biophysics)
 * 64) Deconstruction (Vafa, not Derrida)
 * 65) Swampland--- this is the most important thing going on in string theory, in my biased opinion.
 * 66) Energy loss by charged particles in matter--- Bethe formula, experimental data banks, etc.
 * 67) Hubbard model and High Tc--- the links here are clear, but disputed
 * 68) 'tHooft model 2d gauge theory in large N
 * 69) Schwinger model --- baby version 2d QED
 * 70) Anomaly matching conditions--- these need to be universally understood.
 * 71) 11-d SUGRA Lagrangian + physical stuff
 * 72) 10-d SUGRA Lagrangian + string stuff
 * 73) N=8 4d SUGRA perturbation theory--- this is hot now
 * 74) Spin 3/2 --- full discussion Rarita Schwinger, SUSY
 * 75) Spin 2--- full discussion Pauli Fierz, Einstein
 * 76) Taub NUTs and gravitational KK monopoles
 * 77) Monopoles in gauge theory--- Dirac, Schwinger, Polyakov 'tHooft
 * 78) Widom relations (exponent inequalities saturated below the critical dimension)
 * 79) Clausius Clayperon equation (elementary and well known, but I like this thing--- it's a highlight of 19th century physics)
 * 80) Triple phase boundaries (recent Widom work in the same tradition)
 * 81) Degennes theory (polymers N=0 models)
 * 82) Parisi theory (Spin glasses, replicas, disorder)
 * 83) Off diagonal long range order (Yang, and the rest)
 * 84) Lee model (early renormalization)
 * 85) Khriplovich's style beta-function derivation (physically in terms of polarization)
 * 86) Parisi Kardar Zhang equation (this is great)
 * 87) reaction diffusion system (give real chemical systems--- they're Turing complete)
 * 88) dynamical systems entropy
 * 89) Kolmogorov Turbulence model (not just the scaling--- the correlation functions Kolmogorov Heisenberg style)
 * 90) Polyakov 2-d Turbulence model (what the heck is this--- it's a CFT, it satisfies Euler equation, but is it turbulence?)
 * 91) Kraichnan model (passive scalar advection)
 * 92) LDA approximation (more Kraichnan)
 * 93) randomly stirred fluid (Forster, Nelson, Stevens)
 * 94) Shock waves in compressible fluids--- this is more engineering, but the ideas come from physics, and should be known here.
 * 95) Martin Siggia Rose formalism--- this needs to be updated with modern path integration techniques. They did it without path integrals.
 * 96) Bending DNA recent Siggia
 * 97) Melting DNA--- this is a beautiful recent paper by an obscure author, which is very notable--- the double to single stranded transition is exactly described.
 * 98) Landau singularities--- this is the singularities of Feynman diagrams. Big in the 60s. Dead now.
 * 99) Twistor calculus.
 * 100) Perturbation theory from unitarity (this is hot now)
 * 101) Diffractive Higgs production (recent Veneziano)
 * 102) Dual Resonance model (old Veneziano)
 * 103) Large N_f Nc, (70's Veneziano)
 * 104) QCD sum rules (and all other citation classics--- this is the best of them)
 * 105) Nuclear hadron scattering--- shadowing etc, Cornell conference '72.
 * 106) nonlinear sigma model Gell-Mann Levy
 * 107) nonlinear sigma model in general
 * 108) String equations of motion
 * 109) Mukhamal 8d model of Lifschitz points (everybody needs to know this)
 * 110) Long range statistical models and dimensions (Fisher? It's in Domb and Green)
 * 111) String bits (Susskind 70s)
 * 112) Decoherence formalisms: Feynman-Vernon/Caldera-Leggett
 * 113) Kallen spectral representation and applications
 * 114) Luttinger liquid
 * 115) Pomeron-quark coupling (Scholarpedia seems biased on this point--- pomeron quark coupling seems controversial, but I am not sure)

There are hundreds more topic that need expansion. This list is only those things that I thought of, please feel free to add topics which require mathematical content. I will link to the proper article, and place a short summary of required edits. I will try to do as much as I can on this, because I think it is very important.Likebox (talk) 06:21, 23 February 2010 (UTC)