2know

https://www.google.com/search?safe=active&sxsrf=ALeKk02oB6LyE4ZbHwZmFB-kxQu2UoJkTw%3A1602590215621&ei=B5aFX7q9JeHemAW0rq3IBQ&q=+Katz-Pavlovic&oq=+Katz-Pavlovic&gs_lcp=CgZwc3ktYWIQA1DawwFY2sMBYMHFAWgAcAB4AIABNIgBNJIBATGYAQCgAQGqAQdnd3Mtd2l6wAEB&sclient=psy-ab&ved=0ahUKEwj63JbkwbHsAhVhL6YKHTRXC1kQ4dUDCA0&uact=5

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*

https://en.wikipedia.org/wiki/Path_integral_formulation **M.A. de Gosson, Symplectic Methods in Harmonic Analysis and in Mathematical Physics * Borrelli A. (2009) Spin Statistics Theorem. In: Greenberger D., Hentschel K., Weinert F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg

*Massimi M. (2009) Exclusion Principle (or Pauli Exclusion Principle). In: Greenberger D., Hentschel K., Weinert F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg ******* definite. From this he concluded, as Fierz had done before him, that a field ψ(x) with half-integer spin had to be quantised with anticommutation relations so that, by using the ensuing exclusion principle, an infinite number of negative-energy states could be regarded as being already occupied. In this way, one would in the end recover a physical system with positive energy. To prove the second part of the theorem, Pauli implemented locality by requiring that operators derived from ψ(x) and associated to physical quantities should commute for spacelike separations, i.e. for events which, in some reference frame, occur at the same time in two different places. He showed that, when a field with integer spin was quantized according to anticommutation rules, this condition would lead to a relation implying that the field is identically zero. This result was based on a mathematical argument whose legitimacy was proved only years later. ****** https://en.wikipedia.org/wiki/Descartes%27_theorem

000

ZZZ

ahanorv-casher effect(PRL53)/Lineweaver–Burk equation/conundrum/Golay code/supercuspidal representations/Weil

representation/Pauli–Weisskopf/Levi decomposition/Hankel representation/Wess–Zumino model/Hohenberg-Kohn theorem/cavity method/replica method/frustrated interactions/born-oppenheimer approximation/bethe ansatz/Bloch's

work on wavefunctions in periodic potentials/stability group/W-Curve/Hohenberg-Kohn theorem/non-adiabatic correction/sheaf theory/Serre spectral sequence/spectral sequences/Wu-Yang phase

factor/Aharonov-Bohm phase//Wigner-Eckart Theorem//Dirichlet principle/Hopf theorem/Schreier’s theory of group extensions/Fubini’s theorem/Clausen function/heterotic E8 × E8/Majorana–Weyl fermions/self-dual even lattice/Kac–Moody algebras/group embedding/model building/model building/Casimir invariants /Dynkin indices/heterotic string/K theory/index theorem/loop analysis/De Rham complex/skein relation/vassilief invariants/string coupling/quantum cohomology/non-commutative geometry/combinatorical knot invariants/gromov/witten/connes/vassiliev/kontsevich/donaldson/de rham differential forms/segal functorial quantum mechanics/atiyah-singer index theorem/chern character/moduli space/module(math)/winding number/narain lattices/topological strings/mirror symmetry/holomorphic maps/kahler manifold/sympletic manifold/instanton action/pseudo-holomorphic spheres/pseudodifferential

equations/p-adic dynamical systems/Diophantine geometry/canonical heights/non-Archimedean dynamics/Helmut Hasse’s local-global principle/p-adic Gibbs measures/

fatou set/Sullivan’s no wandering domains theorem/wild recurrent Julia critical points/1-Lipschitz transformations/Kolmogorov’s probability theory/E8 group/narain group/homology/K-theory/van der pol equation/Dawson's integral/lambda calculus/chain geometry/cross ratio/Homogeneous Matrices/affine geometry/novemina/Killing form/Campbell–Baker–Hausdorff theorem/exceptional algebras/module(math)/cryogenic/Fibration(MATH)/ Villarceau CIRCLE/Dupin_cyclide/PoincarE conjecture/nyquist theorem/Leech lattice/Jordan/algebras/esoteric/E8 group/immersion/sundry/segue/Gaussian and Kleinian integers over C/Dickson's  ALGEBRA/ Dixon's ALGEBRA/D4 group/Hamiltonian chains/Hamiltonian circuits/semi-simple Lie algebras/Ruled surfaces/Study’s sphere/Kinematics/Maslov index/Bravais lattice/Earnshaw's Thm/Bott periodicity/Jordan algebra/magic square/topological group/deck transformation/fuchsian group/metaplex/uniformation thm/Pontrjagin classes/signature theorem/encapsulation/homotopy/Borel, Farrell–Jones and Baum–Connes conjectures/cobordism/agnostic/Borel rigidity/fundamental group/Browder–

Novikov–Sullivan–Wall' surgery theory/Semisimple Lie Algebras/spectral decomposition linear algebra/NIkiKOV conjecture/chevalley basis/exceptional Jordan algebra/twisted group algebra/zero divisors/Birch and Swinnerton-Dyer Conjecture/Hodge Conjecture/Existence and Uniqueness Problem for the Navier–Stokes Equations/Poincar´e Conjecture/Mass Gap problem for Quantum Yang–Mills Theory/Metaplectic group/Θ10/ center OF GROUP/split real form / indefinite signature /Heisenberg equation/ classical group/derived sets/cyclides/Pfaff's equation/Weierstrass points/Dirichlet's problem/Jacobi inversion problem/Riemann mapping theorem/uniformization theorem/圈同倫/Virasoro algebra/Riemann surface/principle of permanence of functional equations/vertex algebras/conformal field theory/correlation functions/Heisenberg algebra/Wightman’s axioms/semidirect products/Verlinde formula/twisted K-theory/topological group/Virasoro algebra/semi-stable holomorphic vector bundles/Riemann

surface/Killing Fields/Central Extensions/Bargmann’s Theorem/Virasoro Algebra/Wick Rotation/Highest-Weight Representations/Verma Modules /Kac Determinant/Diff+(S)/vehement/spin sums and Dirac matrices/Kontsevich–Zagier period/Eyring Equation/Cartan subalgebra/Georgi–Glashow model/SO(10) model/Peccei–Quinn symmetry/MacDowell-Mansouri formalism/Coleman-Mandula theorem/Klein geometry/Coleman-Mandula theorem/Einstein-Proca model (e.g. [9,13]), the Einstein-

Proca-Weyl theories or the Maxwell-Chern-Simons-Proca/Saccheri-Legendre theorem/Viete's neusis construction/geometrization conjecture/Dini's flowering surface/

TO BUY:rubik cube/isogeny/

ZZZ

2BS: bell number/stirling and euler-maclaurin/so(n),so(4) and quartnion,so(8) and octonion/laplacian in high div/spherical trig/Hamilton-Jacobi theory/WKB/Gauss-Bonnet/

ZZZ

*Wirtz D, Konstantopoulos K & Searson PC (2011) The physics of cancer:

the role of physical interactions and mechanical forces in metastasis.

Nat. Rev. Cancer 11, 512–522.

*R. F. Streater and A. S. Wightman.  Spin & Statistics, and All That

*the odd quantum by sam treiman

*http://www.staff.science.uu.nl/~gadda001/goodtheorist/

*https://www.thphys.uni-heidelberg.de/~duo/skripten/schmidt_QFT1.pdf

*Three Dimensional Chern-Simons Theory as a Theory of Knots and Links  

*P. Rama Devi, T.R. Govindarajan and R.K. Kaul

*A. F. Wells, Structural Inorganic Chemistry

*Why Chemical Reactions Happen

*Lee, J. M. (2003), Introduction to Smooth manifolds, Graduate Texts in Mathematics, 218

*Rossmann, Wulf (2002), Lie Groups – An Introduction Through Linear Groups

*Fulton, W.; Harris, J. (1991), Representation Theory, A first Course, Graduate Texts in Mathematics, 129

*Hall, Brian C. (2003), Lie Groups, Lie Algebras, and Representations An Elementary *Introduction, Graduate Texts in Mathematics, 222

*Reid, Robert C.; Prausnitz, J. M.; Sherwood, Thomas K. (1977), Properties of Gases and Liquids

*Fifty years of spin: Personal reminiscences.Uhlenbeck, GE (2008)

*Some Properties of Rosette Configurations of Gravitating oBdies in Homographic

Equilibrium". Astronomical Journal. 67 (3): 162–7. Bibcode:1962AJ.....67..162K (http://adsabs.harvard.edu/abs/1962

AJ.....67..162K). doi:10.1086/108686 (https://doi.org/10.1086%2F108686

Fuchs and Schweigert, Symmetries, Lie algebras, and representations: a graduate course for physicist sC.ambridge

*Introduction to Affine Groups Schemes by William Waterhouse

*T. A. Springer et al., Octonions, Jordan Algebras and Exceptional Groups

*V. Moll, The evaluation of integrals: A personal

story, Notices of the AMS 49 (2002), 311–317.

*Les C*-algèbres et leurs représentations, Gauthier-Villars

*P. Ramond, “Algebraic Dreams”, hep-th/0112261

**P. W. Bridgmanm,dimensional analysis,Yale University press, New Haven, 1931

ZZZ

germain/germane/copyright 2017 Shuey Lyn

zzz

2BS: bell number/stirling and euler-maclaurin/so(n),so(4) and quartnion,so(8) and octonion/laplacian in high div/spherical trig/Hamilton-Jacobi theory/WKB/Gauss-Bonnet/homotopy groups/

zzz

Nullstellensatz/Frobenius groups/pons asinomm/Lefschetz

fixed point theorem/Schrδder numbers/Cartan-Killing classification

/Georgi-Glashow SU(5)/BIRKHOFF　VARIETY THM/KNUTH-BENDIX COMPLEXTION/Hauptmodul/Russell–Saunders coupling or LS coupling/orbifold/campanology/

deliberate/holomorphiC/Langevin/icosians/Bott-Duffin theorem/the moment problem/Duffin basis/Lie–Bäcklund transformations/periphractic number/Nernst postulate/

Z

https://en.wikipedia.org/wiki/Spin(3,1)/

http://math.ucr.edu/home/baez/gravitational.html

*R. Hoffmann, Solids and Surfaces: A Chemist’s View of

Bonding in Extended Structures , VCH Publishers, New

York, 1988, pp. 1–7

*D. Kurzydiowski, P. Zaleski-Ejgierd, W. Grochala, R. Hoffmann,

Inorg. Chem. , 2011 , 50 , 3832.

*J. W. Moore and R. G. Pearson, Kinetics and Mechanism ,

3rd ed., John Wiley & Sons, New York, 1981,

pp. 357–363.

*Reaction Mechanisms of Inorganic and

Organometallic Systems

*Introduction and general survey

*Mackey, George (1978). Unitary Group Representations in Physics, Probability and Number Theor

*1) Biological Asymmetry and Handedness, Ciba Foundation Symposium 162, John

Wiley and Sons, 1991

*(Introduction to Ligand Fields,

p. 221. Used by permission from

Brian Figgis

*Orbitals, Terms,

and States , Wiley InterScience

*Laporte

selection rule

B. N. Figgis, “Ligand Field Theory,” in G. Wilkinson, R. D. Gillard, and J. A. McCleverty, eds.

Comprehensive Coordination Chemistry , Vol. 1, Pergamon Press

*https://en.wikipedia.org/wiki/Icosahedral_symmetry#Commonly_confused_groups

*D. Stachel, I. Svoboda and H. Fuess, Phosphorus pentoxide at 233 K, Acta Cryst. C51 (June

1995), 1049–1050

*Andrew Baker, Matrix Groups: An introduction to Lie Group Theory

*Robert Webb’s Stella software http://www.software3d.com/Stella.php

*Group Explorer

*https://en.wikipedia.org/wiki/Unit_ray_representation

*https://en.wikipedia.org/wiki/Helicity_(particle_physics)

*https://en.wikipedia.org/wiki/Group_extension#Central_extension

*Felix Klein’s Lectures on the Icosahedron

*http://math.ucr.edu/home/baez/classical/gravitational.pdf

*http://math.ucr.edu/home/baez/classical/gravitational2.pdf

*[Sh] J. Shurman, Geometry of the Quintic, Wiley, New York, 1997. Available at http://people.reed.edu/~jerry/Quintic/quintic.html

*BK vainshtein modern crystallography

*493 Am. J. Phys., Vol. 61, No. 6, June 1993 

*Boltzmann’s 1877

*http://math.ucr.edu/home/baez/classical/gravitational2.pdf

*https://www.zhihu.com/question/46587733

*https://johncarlosbaez.wordpress.com/2012/05/21/symmetry-and-the-fourth-dimension-part-1/

*https://en.wikipedia.org/wiki/Icosahedral_symmetry#Commonly_confused_groups

*https://en.wikipedia.org/wiki/Littlewood–Richardson_rule

*https://en.wikipedia.org/wiki/Young%27s_lattice

*https://en.wikipedia.org/wiki/Lattice_(order)

*https://en.wikipedia.org/wiki/Symmetric_function

*https://en.wikipedia.org/wiki/Jack_function

*https://en.wikipedia.org/wiki/Schur–Weyl_duality

*https://en.wikipedia.org/wiki/Involution_number

*https://en.wikipedia.org/wiki/Involution_number

*https://en.wikipedia.org/wiki/Cohomology_class

*https://en.wikipedia.org/wiki/Hook_length_formula

*https://en.wikipedia.org/wiki/Graded_algebra

*https://en.wikipedia.org/wiki/Filtered_algebra

*Shurman, Geometry of the Quintic, Wiley, New York, 1997

*https://en.wikipedia.org/wiki/Heyting_algebra

*http://math.ucr.edu/home/baez/noether.html

*Victor Guillemin and Shlomo Sternberg, Variations on a Theme by Kepler, Providence, R.I., American

Mathematical Society, 1990

*http://www.gregegan.net/SCIENCE/ConicSectionOrbits/ConicSectionOrbits.html

*Vladimir I. Arnol'd, Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and

Catastrophe Theory from Evolvents to Quasicrystals

*The Weil representation, Maslov index and theta series

*Weil, André (1964), "Sur certains groupes d'opérateurs unitaires", Acta Math., 111: 143–211

*The geometric Weil representation

*Gurevich, Shamgar; Hadani, Ronny (2005),C anonical quantization of symplectic vector spaces over finite field

*https://en.wikipedia.org/wiki/Operator_algebra

*https://en.wikipedia.org/wiki/Approximately_finite-dimensional_C*-algebra

*https://en.wikipedia.org/wiki/Cartan_connection

*https://en.wikipedia.org/wiki/Mathematical_logic

*https://en.wikipedia.org/wiki/Wiener_filter

*https://en.wikipedia.org/wiki/Wiener_equation

*https://en.wikipedia.org/wiki/Brownian_motion

*https://en.wikipedia.org/wiki/Tauberian_theorem

*https://en.wikipedia.org/wiki/Paley–Wiener_theorem

*https://en.wikipedia.org/wiki/Wiener–Khinchin_theorem

*https://en.wikipedia.org/wiki/Frobenius_endomorphism

*https://en.wikipedia.org/wiki/Cartan_connection

*https://en.wikipedia.org/wiki/Levi-Civita_connection

*http://math.umn.edu/~karl0163/docs/fock.pdf

*https://en.wikipedia.org/wiki/Composite_field

*https://en.wikipedia.org/wiki/Resonance_(particle_physics)

*https://en.wikipedia.org/wiki/Bethe–Salpeter_equation

*http://link.aps.org/doi/10.1103/PhysRevA.83.055802

*https://en.wikipedia.org/wiki/Jaynes-Cummings-Hubbard_model

*https://doi.org/10.1088%2F0953-4075%2F41%2F16%2F161002

*https://en.wikipedia.org/wiki/Magma_(algebra)

*http://www.gap-system.org/~history/Extras/Preston_semigroups.html

*https://link.zhihu.com/?target=https%3A//en.wikipedia.org/wiki/Feynman%25E2%2580%2593Kac_formula

*https://link.zhihu.com/?target=https%3A//en.wikipedia.org/wiki/Gelfand%25E2%2580%2593Naimark%25E2%2580%2593Segal_construction

*Croom, TOPOLOGY

*https://en.wikipedia.org/wiki/Code

*https://en.wikipedia.org/wiki/Hamming_distance

*https://en.wikipedia.org/wiki/Joint_source_and_channel_coding

*https://en.wikipedia.org/wiki/Reed-Solomon_code

*https://en.wikipedia.org/wiki/Turbo_code

*https://en.wikipedia.org/wiki/LDPC_code

*https://en.wikipedia.org/wiki/Binary_Golay_code

*https://en.wikipedia.org/wiki/Hamming_numbers

*https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

*https://en.wikipedia.org/wiki/Binary_Golay_code

*https://en.wikipedia.org/wiki/Group_testing

*M. Bander and C. Itzykson, “Group theory and the hydrogen atom (I)”. Rev. Mod. Phys. 38: 330–345 (1966).

*https://en.wikipedia.org/wiki/Canonical_quantization#Issues_and_limitations

*https://doi.org/10.1016%2FS0031-8914%2846%2980059-4

*https://en.wikipedia.org/wiki/Neural_networks

*Levi decomposition

*https://en.wikipedia.org/wiki/Homology_group

*https://en.wikipedia.org/wiki/Symmetric_polynomial

*https://en.wikipedia.org/wiki/Sigma_model

*