start edit
https://en.wikipedia.org/wiki/Spectral_gap_(physics) https://en.wikipedia.org/wiki/Duality_gap +
https://en.wikipedia.org/wiki/Doubly_periodic_function https://en.wikipedia.org/wiki/Fundamental_pair_of_periods
Group diagrams edit
https://commons.wikimedia.org/wiki/Category:Mathematical_diagrams https://commons.wikimedia.org/wiki/Category:Commutative_diagrams https://commons.wikimedia.org/wiki/Category:Group_theory https://commons.wikimedia.org/wiki/File:Projective-representation-lifting.svg +] + + + + + +
groups: https://en.wikipedia.org/wiki/Bézout's_identity
Rings: https://en.wikipedia.org/wiki/Chinese_remainder_theorem
https://en.wikipedia.org/wiki/Weierstrass_transform#Generalizations https://en.wikipedia.org/wiki/Shift_operator https://en.wikipedia.org/wiki/Operator_(physics)#The_exponential_map +
https://en.wikipedia.org/wiki/Chern-Simons_theory#HOMFLY_and_Jones_polynomials https://en.wikipedia.org/wiki/Weyl_character_formula#The_SU(2)_case
https://en.wikipedia.org/wiki/Representation_theorem
https://en.wikipedia.org/wiki/Vanishing_theorem
https://en.wikipedia.org/wiki/Analytic_torsion https://en.wikipedia.org/wiki/Crooks_fluctuation_theorem
https://en.wikipedia.org/wiki/Agoh-Giuga_conjecture https://en.wikipedia.org/wiki/Daniel_da_Silva_(mathematician) https://en.wikipedia.org/wiki/Euler's_identity#Generalizations
https://en.wikipedia.org/wiki/Crenel_function https://en.wikipedia.org/wiki/Montgomery's_pair_correlation_conjecture
https://en.wikipedia.org/wiki/Cyclotomic_polynomial https://proofwiki.org/wiki/Reciprocals_of_Odd_Numbers_adding_to_1
https://en.wikipedia.org/wiki/Chebyshev_function#The_Riemann_hypothesis https://en.wikipedia.org/wiki/Explicit_formulae_(L-function)#Weil's_Explicit_Formula https://en.wikipedia.org/wiki/Hilbert–Pólya_conjecture https://mathoverflow.net/questions/62816/the-guinand-weil-explicit-formula-without-entire-function-theory?rq=1
https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities
https://en.wikipedia.org/wiki/Generating_function https://en.wikipedia.org/wiki/Table_of_Newtonian_series
for +
Hodge duality->Poincaré duality->Grothendieck local duality->Serre duality
https://en.wikipedia.org/wiki/Dedekind_psi_function https://mathoverflow.net/questions/14083/modular-forms-and-the-riemann-hypothesis
"Index theory" edit
Genus Stuff edit
Riemann-Roch_theorem: Line bundle-Riemann surface Vector Bundle-Complex manifold Quotient stack sheaf-Orbifold Chain-complex sheaf-Scheme Arithmetic
Degenerancy theory edit
Poincaré–Hopf theoremHairy ball theorem
Banach fixed point theorem(existence and uniqueness) Brouwer_fixed-point_theorem(existence) Fixed point degree
There are several fixed-point theorems which come in three equivalent variants: an algebraic topology variant, a combinatorial variant and a set-covering variant. Each variant can be proved separately using totally different arguments, but each variant can also be reduced to the other variants in its row. Additionally, each result in the top row can be deduced from the one below it in the same column.[1]
Algebraic topology | Combinatorics | Set covering |
---|---|---|
Brouwer fixed-point theorem | Sperner's lemma | Knaster–Kuratowski–Mazurkiewicz lemma |
Borsuk–Ulam theorem | Tucker's lemma | Lusternik–Schnirelmann theorem |
Hall's marrriage theorem equivalences
Cayley's theorem equivalencesWagner-preston theorem (Cayley' theorem on inver semigroup)+
Covering/packing-problem pairs | ||||||||
---|---|---|---|---|---|---|---|---|
|
||||||||
group theory: definitions basics factsnon basic facts
Centralizer-Normalizer Orbit stabilizer coset-index
Fundamental theorem of abelian groups Fundamental theorem of cyclic groups Fundamental theorem of free groups Jordan–Hölder theorem Finitely generated abelian group
Rodrigues's formula Li's criterion
Szegő_limit_theorems Jensen's formula five value theorem
https://en.wikipedia.org/wiki/Fredholm's theorem Fredholm alternative Farkas_lemma Hyperplane separation theorem Hanh Banach separation theorem Positive-definite matrix Positive-definite kernel Positive definiteness
homology-homotopy dictionary+
number field-function field dictionary
Kapranov-Reznikov-Mazur dictionary/arithmetic topology
+
+
+
+
+
+
Diophantine dictionary/Arithmetic dynamics
algebraic geometry dictionary
+
wu-yang dictionary
elliptic-parabolic dictionary
feynman-intersection number dictionary-like
petterson-weil volume+ witten's volume orbifolds volume orbifold euler characteristic+
varieties: Grassman Segre veronese
global-local homology global-local homotopy +
nowhere differentiable: everywhere continuos, nowhere continuos
mle-entropy
euler-lagrange-gauss-principle
(Elliptic function-Elliptic curve) (Modular form-Modular curve)
Arithmetic geometry Fermat's squares theorem Minkowski's theorem + Gauss circle problem Dirichlet's divisor problem
Class field theory
Class number
Class number formula
List of number fields with class number one
Lists of discriminants of class number 1
Stark-Heegner_theorem
Kronecker-Weber_theorem
Kummer theory
Fundamental discriminant
+
+
Perron's formulaShimura correspondence
Winding number-Eisenbud Levine Khimshiashvili signature formula
Roth's_theorem-Duffin-Schaeffer conjecture
Kutsenov trace formula-Gutzwiller trace formula
Min-Max theoremMax-min_inequality
Kolmogorov equation-Fokker Planck equation
Koopman operator-Perron-Frobenius operator
not recursive function not computable function not ZFC-dependent function bound+
Feller-Tornier constant + Pólya conjecture Chebyshev's bias + + Goldfeld conjecture + Parity_problem
Bateman-Horn conjecture square free distribution +
Minakshisundaram–Pleijel | ||
Lovelock |
https://en.wikipedia.org/wiki/Homology_(mathematics)
Manifold | Euler No. χ |
Orientability | Betti numbers | Torsion coefficient (1-dimensional) | |||
---|---|---|---|---|---|---|---|
Symbol[3] | Name | b0 | b1 | b2 | |||
Circle (1-manifold) | 0 | Orientable | 1 | 1 | N/A | N/A | |
Sphere | 2 | Orientable | 1 | 0 | 1 | none | |
Torus | 0 | Orientable | 1 | 2 | 1 | none | |
Projective plane | 1 | Non-orientable | 1 | 0 | 0 | 2 | |
Klein bottle | 0 | Non-orientable | 1 | 1 | 0 | 2 | |
2-holed torus | −2 | Orientable | 1 | 4 | 1 | none | |
g-holed torus (Genus = g) | 2 − 2g | Orientable | 1 | 2g | 1 | none | |
Sphere with c cross-caps | 2 − c | Non-orientable | 1 | c − 1 | 0 | 2 | |
2-Manifold with g holes and c cross-caps (c > 0) | 2 − (2g + c) | Non-orientable | 1 | (2g + c) − 1 | 0 | 2 |
- NOTES:
- For a non-orientable surface, a hole is equivalent to two cross-caps.
- Any 2-manifold is the connected sum of g tori and c projective planes. For the sphere , g = c = 0.
Legendre form | hypergeometric differential equation | |
weierstrass form | Picard–Fuchs differential equation | |
Riemann form | Riemann's differential equation |
???????????????
- https://en.wikipedia.org/wiki/Modular_elliptic_curve
- https://en.wikipedia.org/wiki/Weierstrass's_elliptic_functions#General_theory
- https://en.wikipedia.org/wiki/Poincaré–Bendixson_theorem
- https://en.wikipedia.org/wiki/Nielsen-Thurston_classification
- https://en.wikipedia.org/wiki/Wirtinger_derivatives
- https://en.wikipedia.org/wiki/Creation_and_annihilation_operators
Volume form + Connection_form torsion form curvature form + spin connection khäler form + Solder form
Poincaré series Igusa zeta function
Character theory Weyl character formula Kirillov_character_formula
Representation theory Representation of Lie algebra Representation of Lie group Representation of finite groups ℓ-adic representations
Hyperbolic geometryHyperbolic manifold++
{5,5}-tilling-Poincaré Sphere+
Abel's theorem converse Abel's theorem
- invariant factors + companion matrix yields Frobenius normal form (aka, rational canonical form)
- primary decomposition + companion matrix yields primary rational canonical form
- primary decomposition + Jordan blocks yields Jordan canonical form (this latter only holds over an algebraically closed field)
- rngs ⊃ rings ⊃ commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields
zeta table edit
q | q | q | ||
q | ||||
convergence stuff edit
as | p | d | |
LLN | T | T | T |
LIL | F | T | T |
CLT | F | F | T |
Pointwise continuity | x | x | x |
Uniform continuity | x | x | |
equicontinuity | x | x | |
Uniform equicontinuity | x |
PNT | Landau PNT |
RH | Goss zeta function |
Hilbert's reciprocity | Artin's recirpocity |
abc conjecture | Mason–Stothers_theorem |
falting's theorem | function field falting's theorem |
Geodesics | PGT | Selberg zeta function | selberg trace formula | ||
P-adic | P-adic L-function | ||||
Motives | Motivic zeta function | Motivic L-function | |||
Varietes | Weil Conjectures++ | Local zeta function | Hasse-Weil zeta function+ | ||
Schemes | Grand RH¿? | arithmetic zeta function | |||
Ideals | ERH | Dedekind zeta function | |||
Characters | GRH | Dirichlet L-function | |||
Naturals | RH | PNT | Riemann zeta | Explicit_formulae |
Selberg class Abstract analytic number theory
PNT | RH |
|
|
Counting | LLN | CLT | Zeros | |
naturals | primes | PNT | RH | |
naturals | factors | Hardy ramanujan | Erdős-Kac_theorem | |
Geodesics | primes | PGT | ++ | |
Geodesics | factors | ? | ||
Elliptic curves | factors | ? |
+
+
One can view Selberg’s theorem as a sort of Fourier-analytic variant of the Erdös-Kac theorem.
PNT scaled models++
mertens=/=PNT+
+
g=0 | g=1 | g>1 | |
homeomorphism | |||
Universal cover | |||
fundamental group | 0 | ||
automorphism | Hurwitz's bound | ||
moduli | Example | j-invariat/cross ratio | 3g-3 |
curvature | 0 | 1 | -1 |
Diophantine | Mordell-Weil theorem+ | Faltings's theorem |
(complex disk,plane,sphere) +
automorphisms | ||
n>0:TOP=PL=DIFF
n>3:TOP=\=PL=DIFF
n>6:TOP=\=PL=\=DIFF
True | False | |||||
TOP | PL | DIFF | TOP | PL | DIFF | |
Manifold classification (MC) | 1,2,3 | 1,2,3 | 1,2,3 | n>3 | n>3 | n>3 |
Simple connected closed MC | 1,2,3,5 | 1,2,3 | 1,2,3 | n>3 | n>3 | |
Poincaré Conjecture | 1,2,3,4,5,... | 2,3,?,5,... | 2,3,?,5,6 | n>6 |
TOP | PL | DIFF | ||
n=2 | Manifold classification (MC) | True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
n=2 | Simple connected closed MC | True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
n=2 | Poincaré conjecture | True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
True Uniformization Poincare&koebe |
n=3 | Manifold classification (MC) | True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
n=3 | Simple connected closed MC | True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
n=3 | Poincaré conjecture | True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
True Thurston's geometrization Perelman |
n=4 | Manifold classification (MC) | False Uncountable Markov |
False Uncountable Markov |
False Uncountable Markov |
n=4 | Simple connected closed MC | False untriangulable & uncountable Casson & Donaldson |
False untriangulable & uncountable Casson & Donaldson | |
n=4 | Poincaré conjecture | True Cobordism Freedman |
||
n=5 | Manifold classification (MC) | False Uncountable Markov |
False Uncountable Markov |
False Uncountable Markov |
n=5 | Simple connected closed MC | True Barden |
False untriangulable Manolescu |
False untriangulable Manolescu |
n=5 | Poincaré conjecture | True Engulfing Newman |
True Cobordism Smale |
True Cobordism Smale |
n=6 | Manifold classification (MC) | False Uncountable Markov |
False Uncountable Markov |
False Uncountable Markov |
n=6 | Simple connected closed MC | False untriangulable Manolescu |
False untriangulable Manolescu | |
n=6 | Poincaré conjecture | True Engulfing Newman |
True Cobordism Smale |
True Cobordism Smale |
n>=7 | Manifold classification (MC) | False Uncountable Markov |
False Uncountable Markov |
False Uncountable Markov |
n>=7 | Simple connected closed MC | False untriangulable Manolescu |
False untriangulable Manolescu | |
n>=7 | Poincaré conjecture | True Engulfing Newman |
True Cobordism Smale |
False Exotic sphere Milnor |
Analogies: Quine McCluskey algorithmBuchberger's algorithm
Correspondences:
algebraic sets & Ideals
Field subextension & Galois Subgroups
Space covering & Fundemantal group
+
+
+
Modular forms & Elliptic curves
Automorphic forms & Algebraic curves
Elliptic modular forms & Group representations
Geometric langlands
Kobayashi–Hitchin correspondence
Simpson correspondence
Riemann-Hilbert correspondence
Robinson-Schensted correspondence
Shimura correspondence-Theta correspondence
Enumerative invariants:
Sympletic category:
Donaldson invariants
Seiberg–Witten invariants
Gromov-Witten invariants
FJRW theory
Algebraic category:
Donaldson–Thomas
+
characterization: Gamma function+ Determinant exponential function
Obstructions characteristic classes:
- homotopy=simple homotopy: Whitehead torsion+
- homeorphism=PL homeomorphism: Kirby-Siebenmann_class+
- homeomorphims=homotopic homeomorphism:Reidemeister torsion
- homeomosphism=homological homeomorphism?:Euler class
- vector bundle morphism=vector bundle isomorphism: Stiefel-Whitney_class
- complex vector bundle morphism=complex vector bundle isomorphism:Chern-class (unitary group)
+
Pontryagin_class (orthogonal group)+++
- Todd classreciprocal characteristic class
- Segre class-inverse chern class
- Hasse invariant
- Manin obstruction
Generalizations: (Hodge conjecture-Arithmetic Hodge Conjecture) (Milnor conjecture-Thom conjecture) (Witten conjecture-Virasoro conjecture) (K theory-L theory) (Pontryagin_duality-Tannaka-Krein duality) (Maximun principle-Hopf's Maximum principle) (Padé series-Laurent series-Puiseux series) (Weierstrass factorization-Mittag-Leffer's factorization) (Stone-Weierstrass theorem-Arakelyan's_theorem) (Cantor's_paradox-Ordinal Cantor's paradox(Introduction to Mathematical Logic Mendhelson page 2))(Stone's theorem-Stone-von Neumann theorem) (Morse theory-Picard-Lefschetz theory) (Invariant theory-Geometric invariant theory) (https://en.wikipedia.org/wiki/Differential_Galois_theory)
(Farkas's lemma-Fredholm alternative) (sdf matrix-sdf kernel)
Martingale CLT Functional integralPath integral
- Gibbs entropy-LK entropy-arithmetic entropy?-maximun entropy-openprob entropy
- AEP+LLN+CLT=LAN
-
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution
Vector bundles on algebraic curves Birkhoff–Grothendieck theoremAtiyah-Birkhoff–Grothendieck theorem
Bott periodicity&Hurwitz's_theorem Bott_periodicity_theorem Hurwitz theorem
Vector bundles on algebraic curves Birkhoff–Grothendieck theoremAtiyah-Birkhoff–Grothendieck theorem
Hesisenberg group transform Special linear group transform +?
Special_unitary_group (spin group) + +2 +3 +4 +5
String group + +2 anomaly conformal invariants + +2
- soliton (localised in space)(fixed points of the flow?)
- breather (periodic soliton), oscilon (standing periodic soliton), kink(steady state periodic soliton)
- ADHM instanton
- Instanton(localised in time soliton)(1d:tunneling,2d:vortices,3d:higgs field-TP monopole, 4d: gauge bundle)
- Renormalon(Borel istanton)
- Cotangent localization
Helmholtz decomposition FLRW decomposition Ricci tensor decomposition Riemann tensor decomposition Electromagnetic tensor decomposition+
cauchy-pompieu decomposition poloidal decomposition clebsch decomposition
Covariance matrix Covariance process +
variational quotients edit
Dirichlet eigenvalue Rayleigh quotient Variational method Fisher's linear discriminant Poincaré constant Cheeger constant
Poincaré inequality Bauer Fike theorem
Min-max theorem Minimax theorem Max-min inequality Duality gap Lagrange multiplier
Geometric_phase Fubini-Study_metric Fisher_information_metric
Coarea formula Smooth coarea formula coarea+ coarea+
Distance preserving Angle preserving Area preserving Volume preserving + Sympletic preserving + +
Knot group Link group Braid group
Knot theory Link theory Braid theory Ribbon theory +
Homology group Homotopy group Holonomy group
Cohomology group Cohomotopy group
Homological algebra Homotopical algebra
stable unitary group stable orthogonal group J-homomorphism
Riemann zeta function Hurwitz zeta function Polylogarithm
Eta invariant Dirichlet_eta_function [2] 1+2+3+4+... Riemann+Euler-Maclaurin Darboux's formula
Analytic torsion Heat kernel signature
Signature operator Atiyah Singer index theorem+
Supersymmetric atiyah Singer index theorem + +2 +3 +?
Equivalences:Abel–Plana_formula<=>Euler–Maclaurin_formula<=>Poisson summation formula
Singular Kernel Regularization
Riemman, Ricci, scalar curvature +
isothermal conformal uniformization isothermal/conformal? Ricci flow
Inclusion-exclusion principle Isomorphism theorems
- atiyah-singer proof techniques: pseudodifferential operator, cobordism, k theory, heat operator
- https://en.wikipedia.org/wiki/Borel_summation (best summation)
- https://en.wikipedia.org/wiki/Padé_approximant (best rational approximant)
- https://en.wikipedia.org/wiki/Category:Mathematics-related_lists
- https://en.wikipedia.org/wiki/List_of_cohomology_theories +
- https://en.wikipedia.org/wiki/Vanishing_theorem
- https://en.wikipedia.org/wiki/Fixed-point_theorem#List_of_fixed-point_theorems
- https://en.wikipedia.org/wiki/List_of_zeta_functions ++
- https://en.wikipedia.org/wiki/Trace_formula
- https://en.wikipedia.org/wiki/List_of_dualities
- https://en.wikipedia.org/wiki/Category:Duality_theories
- https://en.wikipedia.org/wiki/List_of_complex_and_algebraic_surfaces
- https://en.wikipedia.org/wiki/List_of_small_groups
- https://en.wikipedia.org/wiki/List_of_prime_knots (https://en.wikipedia.org/wiki/Knot_tabulation)
- https://en.wikipedia.org/wiki/List_of_mathematical_knots_and_links
- https://en.wikipedia.org/wiki/List_of_manifolds
https://en.wikipedia.org/wiki/Uniqueness_theorem
- https://en.wikipedia.org/wiki/Classification_theorem
- https://en.wikipedia.org/wiki/Complete_set_of_invariants
- https://en.wikipedia.org/wiki/Invariant_(mathematics)
- (https://en.wikipedia.org/wiki/Invariant_theory)
- https://en.wikipedia.org/wiki/Enriques-Kodaira_classification#Invariants_of_surfaces
- https://en.wikipedia.org/wiki/Decomposition_(disambiguation)
- (complex disk,plane,sphere)
- algebraic classification 2-manifolds: sum connected toris,sum connected projective plane, sphere, geometric classification, topological classification, combinatoric classification
- https://en.wikipedia.org/wiki/Holonomy#The_Berger_classification
- https://en.wikipedia.org/wiki/Wigner's_classification
- https://en.wikipedia.org/wiki/Bianchi_classification
- https://en.wikipedia.org/wiki/Petrov_classification
- https://en.wikipedia.org/wiki/Classification_of_Clifford_algebras
- https://en.wikipedia.org/wiki/Enriques–Kodaira_classification
- https://en.wikipedia.org/wiki/Bernstein–Zelevinsky_classification
- https://en.wikipedia.org/wiki/Langlands_classification
- https://en.wikipedia.org/wiki/Segre_classification
- https://en.wikipedia.org/wiki/Crystal_system#Classification_of_lattices
- https://en.wikipedia.org/wiki/Painlevé_transcendents
- https://en.wikipedia.org/wiki/List_of_finite_simple_groups
- complexity classes lists: list complexity classes+complexity zoo
[https://en.wikipedia.org/wiki/Schrödinger_equation#Time_indep endent ]
Plane partition number partition Multiplicative_partition (unordered factorization)
Numerical methods: Garlekin Homotopy analysis Finite difference Finite element Finite volume ≈
Physics edit
https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)
https://physics.stackexchange.com/questions/295714/whats-the-relation-between-path-integral-and-dyson-series http://bolvan.ph.utexas.edu/~vadim/Classes/2011f/dyson.pdf
https://en.wikipedia.org/wiki/Quantum_invariant https://en.wikipedia.org/wiki/Periodic_table_of_topological_invariants
https://en.wikipedia.org/wiki/Bose_gas https://en.wikipedia.org/wiki/Gas_in_a_box https://en.wikipedia.org/wiki/Gas_in_a_harmonic_trap
Dilaton Perelman's renormalization Perleman's entropy Perelman's fluctuation Quantropy Jacobson's entropic field Verlinde's entropic force [4]
Jacobson | ||||
Verlinde |
velocity limit: light velocity entropy limit: bekenstein bound
Unruh radiation Hawking radiation +
+ Locality breaker: EPR paradox Unitarity breaker: BHI paradox causality breaker: relativity
Newton | ---- | HJ | Koopman–von Neumann |
Ehrenfest theorem | Schrodinger | Bhom | Moyal |
GR | ADM | EHJ | chern-simmonns? |
Crystallographic periodic table crystal structure
Bravais lattice | Wigner-Seitz_cell |
Recriprocal lattice | Brillouin zone |
ΛCDM common observations:
SNIa
CMB
H(z)
BAO
LSS
Planck spacecraft
+
standard candle
standard ruler
Hamilton Jacobi_equation Circulation Biot-Savart
Kutta Joukowski theorem Magnus effect Vorticity equation
Kelvin's circulation theorem tao's post Euler fluid equations Hamiltonian fluid mechanics Madelung equations
https://en.wikipedia.org/wiki/Category:Scattering
https://en.wikipedia.org/wiki/Moiré_pattern https://en.wikipedia.org/wiki/Bragg's_law https://en.wikipedia.org/wiki/Compton_scattering
https://en.wikipedia.org/wiki/List_of_quasiparticles https://en.wikipedia.org/wiki/List_of_particles
mass oscilation | charge oscillation | spin oscilations |
PhononRotonMaxon | polarons | magnons |
Molecular partition function + + +
volumetric entropy surface entropy gas entropy + + +
Bose-Einstein statistics | Fermi-Dirac statistics | anyon statistics | braid statistics |
boson | fermion | anyon | plekton |
https://en.wikipedia.org/wiki/Scale-free_ideal_gas
https://en.wikipedia.org/wiki/Bragg's_law
- https://en.wikipedia.org/wiki/Chapman-Enskog_theory(https://en.wikipedia.org/wiki/Navier-Stokes_equations https://en.wikipedia.org/wiki/Boltzmann_equation)
Non-rotating (J = 0) | Rotating (J ≠ 0) | |
Uncharged (Q = 0) | Schwarzschild | Kerr |
Charged (Q ≠ 0) | Reissner–Nordström | Kerr–Newman |
---
Minkowski | ||
De Sitter | ||
Anti De sitter | ? |
Group contractionQuantization commutes with reduction
D'Alembert->KdV Hierarchy/Dirac operator->BBGKY
Hamiltonian fluid mechanics Madelung equation De_Broglie–Bohm_theory Convection diffusion equation Langevin dynamics
Dyson Series + Functional determinant
Electromagnetism Gravitoelectromagnetism + Kaluza-klein theory Yang-Mills theory
Thomas precession | Gravitational Thomas precession |
Larmor precession++? | de Sitter precession |
Total angular momentum quantum operator | Total angular momentum tensor |
Einstein–de Haas effect |
Bohr-Sommerfeld EBK-Bohr-sommerfeld cyclotron Bohr-Sommerfeld
Aharonov-Bohm effect Landau quantization
T*C->Poison bracket
T*M_g->ADM bracket
+
- https://en.wikipedia.org/wiki/Supersymmetry_nonrenormalization_theorems
- https://en.wikipedia.org/wiki/Loop_representation_in_gauge_theories_and_quantum_gravity
Black hole: Black hole radiation dark matter
Cosmic Backgrounds:
Relics:
Photon(CMB)
Neutrino
Gravitation
DEBRA:
Infrared
X-ray
Extragalactic light
Radio
Gamma-ray
CMB
Angles: Weinberg Peccei–Quinn GIM CKM PMKS +
Planck temperature Hagedorn temperature +
Noether's Theorem extensions Wald entropy formula++
stringification=categorization
Mode of decay | Daughter nucleus | |
---|---|---|
Decays with emission of nucleons: | ||
Alpha decay | (A − 4, Z − 2) | |
Proton emission | (A − 1, Z − 1) | |
Neutron emission | (A − 1, Z) | |
Double proton emission | (A − 2, Z − 2) | |
Spontaneous fission | — | |
Cluster decay | (A − A1, Z − Z1) + (A1, Z1) | |
Different modes of beta decay: | ||
β− decay | (A, Z + 1) | |
Positron emission (β+ decay) | (A, Z − 1) | |
Electron capture | (A, Z − 1) | |
Bound state beta decay | (A, Z + 1) | |
Double beta decay | (A, Z + 2) | |
Double electron capture | (A, Z − 2) | |
Electron capture with positron emission | (A, Z − 2) | |
Double positron decay | (A, Z − 2) | |
Transitions between states of the same nucleus: | ||
Isomeric transition | (A, Z) | |
Internal conversion | (A, Z) |
Nuclide radioactive decay map
Nucleosynthesis periodic table
[5]
Nuclear physics |
---|
- ^ Nyman, Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354, doi:10.4169/amer.math.monthly.120.04.346, JSTOR 10.4169/amer.math.monthly.120.04.346, MR 3035127
- ^ Richeson (2008)
- ^ Weeks, J.R.; The Shape of Space, CRC Press, 2002.