trepidation
2019年1月11日 星期五
2019年1月1日 星期二
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
00
*
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
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*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)/
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*R. Hoffmann, Solids and Surfaces: A Chemist’s View of
Bonding in Extended Structures , VCH Publishers, New
York, 1988, pp. 1–7
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Inorg. Chem. , 2011 , 50 , 3832.
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pp. 357–363.
*Reaction Mechanisms of Inorganic and
Organometallic Systems
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*Mackey, George (1978). Unitary Group Representations in Physics, Probability and Number Theor
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Wiley and Sons, 1991
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p. 221. Used by permission from
Brian Figgis
*Orbitals, Terms,
and States , Wiley InterScience
*Laporte
selection rule
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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
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*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
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*https://en.wikipedia.org/wiki/Wiener_equation
*https://en.wikipedia.org/wiki/Brownian_motion
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*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
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*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
*
筆記0101
Dictyostelium discoideum
fibroblasts
D. discoideum
adenosine 30 ,50 -monophosphate (cAMP
pseudopod
trepidation
狄拉克 (Dirac) 寫於1932年的一篇論文《The Lagrangian in Quantum Mechanics》啟發了他。在該論文中,狄拉克成功把振幅寫成路徑積分的形式。可是,狄拉克只寫下了形式,並沒有展示怎樣以路徑積分作實際計算。由於每一路徑為一時間函數,路徑空間是一無限維空間。所以路徑積分是一個對無限多個變量作的積分,實際計算並不容易。費曼克服了這些困難,發展了一套計算路徑積分的技巧。
通常來說,能帶理論是建立在單電子近似基礎上的,不僅忽略了電聲子相互作用,而且認為價電子在晶體中的運動是彼此獨立的,因此電子間的關聯是被忽略掉的,在電子間關聯作用不是很強的時候,能帶理論是一個很有效的理論,能夠對多數材料體系的導電性(即金屬,半金屬,半導體,絕緣體)作出較好的預言。但是對一些過渡金屬化合物(如:MnO)特性的解釋往往是失敗的。這是因為在窄能帶體系中電子之間的關聯作用是十分重要的,電子從一個局域原子軌道運動到另一個原子軌道上時,必須要考慮到後一軌道是否被其他電子佔據,如果已經被佔據,則應當計入同一原子周圍兩個電子之間的庫侖作用,而這一作用將使能帶狀態發生顯著的變化。
fibroblasts
D. discoideum
adenosine 30 ,50 -monophosphate (cAMP
zeeman是磁場
stark鋼鐵人
是電場
異常季曼效應藥用自旋解釋
羔羊位移要用QED
trepidation
狄拉克 (Dirac) 寫於1932年的一篇論文《The Lagrangian in Quantum Mechanics》啟發了他。在該論文中,狄拉克成功把振幅寫成路徑積分的形式。可是,狄拉克只寫下了形式,並沒有展示怎樣以路徑積分作實際計算。由於每一路徑為一時間函數,路徑空間是一無限維空間。所以路徑積分是一個對無限多個變量作的積分,實際計算並不容易。費曼克服了這些困難,發展了一套計算路徑積分的技巧。
通常來說,能帶理論是建立在單電子近似基礎上的,不僅忽略了電聲子相互作用,而且認為價電子在晶體中的運動是彼此獨立的,因此電子間的關聯是被忽略掉的,在電子間關聯作用不是很強的時候,能帶理論是一個很有效的理論,能夠對多數材料體系的導電性(即金屬,半金屬,半導體,絕緣體)作出較好的預言。但是對一些過渡金屬化合物(如:MnO)特性的解釋往往是失敗的。這是因為在窄能帶體系中電子之間的關聯作用是十分重要的,電子從一個局域原子軌道運動到另一個原子軌道上時,必須要考慮到後一軌道是否被其他電子佔據,如果已經被佔據,則應當計入同一原子周圍兩個電子之間的庫侖作用,而這一作用將使能帶狀態發生顯著的變化。
Griffiths 說
在量子立學理
特徵值之間月簽的機率是零
所以
月千一定是因為外加的點磁場
但是在場論理
有真空漲落的影響
所以會有自發福社
秀豪有談到
相變的關聯常數的問題
序參量
還有一級相變
二級相變
fermi surface
就是費米子填滿的上限
以上都沒有費米子
再轉到動量空間
Shu
我完全不懂
HE3 或 HE4 3k7
的超流體是怎麼來的
如果在常溫中視導體的東西
在低溫時變成絕緣體
這就叫做mott insulator
屬於強關聯體系
通常來說,能帶理論是建立在單電子近似基礎上的,不僅忽略了電聲子相互作用,而且認為價電子在晶體中的運動是彼此獨立的,因此電子間的關聯是被忽略掉的,在電子間關聯作用不是很強的時候,能帶理論是一個很有效的理論,能夠對多數材料體系的導電性(即金屬,半金屬,半導體,絕緣體)作出較好的預言。但是對一些過渡金屬化合物(如:MnO)特性的解釋往往是失敗的。
我以前以為
奇異值分解
和jordan form
沒有用
我錯了
有的物質電阻隨溫度降低反而升高,這就是Kondo現象。這屬於強相互作用體系,單電子為基礎的能帶理論解釋不了。
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