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Wave-particle duality (7391 bytes)
1: In [[physics]], '''wave-particle duality''' holds that [[light]] and [[matter]] simultaneo... 3: <!--This duality merges the [[theory|theories]] of [[Christiaan Hu... 28: ...rimenters have assumed arguments of wave-particle duality and have assumed the validity of deBroglie's equa... 33: In [[quantum mechanics]], the wave-particle duality is explained as follows: every system and particl... 35: ...namics]], Richard Feynman shows the wave-particle duality of photons and electrons is an illusion. In his v... U-duality (669 bytes) 1: ...be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometr... S-duality (2311 bytes) 1: ...g theory|string theories]], or [[M-theory]]. An S-duality transformation maps the states and vacua with [[c... 3: ...ase of four-dimensional quantum field theories, S-duality was understood by [[Ashoke Sen]], [[Nathan Seiber... 5: Two more examples come from string theory: S-duality relates [[type IIB string theory]] with the coupl... 7: S-duality has been rigorously shown to hold in some [[latti... 9: ... U(1) ), then it's dual via the [[Kramers-Wannier duality]] to a model where the vertices take on values in... T-duality (1450 bytes) 1: ...ory, and the two [[heterotic string]] theories. T-duality transformations act on spaces in which at least o... 3: ...ed once around the direction in question. Under T-duality, it will be mapped to a IIB string which has mome... 8: ... be proved invariant under this operation, too. T-duality acting on [[D-branes]] changes their dimension by... 10: ...d that [[mirror symmetry]] can be understood as T-duality applied to three-dimensional toroidal fibres of t... 12: '''Also see''': [[S-duality]], [[U-duality]], [[mirror symmetry]] Duality (1771 bytes) 1: ...[[pair]] – a grouping of two. The word '''''duality''''' has a variety of different meanings in diffe... 3: ...he [[Moche]] of Peru and the Chinese of China, '''duality''' is the premise that everything has an opposing... 4: ...alent. See [[duality (physics)]], [[wave-particle duality]]. 5: * [[Duality (projective geometry)]]. 6: ... duality occurring in mathematics are listed at [[duality (mathematics)]]. Mysterious duality (1246 bytes) 1: In [[theoretical physics]], '''mysterious duality''' is a set of mathematical similarities between ... 3: ...ezzo surfaces match the [[Weyl group]] of the [[U-duality group]] of the corresponding compactification of ... Duality (physics) (1828 bytes) 1: In modern [[physics]], '''duality''' most often refers to the [[paradigm]] underlyi... 3: ...ght. Therefore one speaks of the [[wave-particle duality]]. 5: This duality also implies that [[light]] and [[electromagnetic... 7: ...here this requirement applies. Other fields where duality is encountered in this sense are [[statistical me... 9: Duality can lead to counterintuitive conclusions. For exa... Duality (mathematics) (2107 bytes) 1: ..., mostly, without there being a single ''master'' duality. Generally speaking, dualities translate concepts... 3: ...ample here is the [[duality (projective geometry)|duality in projective geometry]]: given any theorem in pl... 5: **[[duality (order theory)|duality in order theory]] 8: ...ry theory]] that underlies these dualities, see [[duality (category theory)]] and [[dual (category theory)]... 10: **[[Pontryagin duality]], relating certain [[abelian group]]s to other a... Poincaré duality (5919 bytes) 1: In [[mathematics]], the '''Poincaré duality''' theorem is a basic result on the structure of ... 5: A form of Poincaré duality was first stated, without proof, by [[Henri Poinc... 7: ...up]] and [[cap product]]s and formulated Poincaré duality in these new terms. 11: Poincaré duality was classically thought of in terms of dual [[tri... 27: The modern statement of the Poincaré duality theorem is in terms of homology and cohomology: i... Duality (album) (567 bytes) 1: '''''Duality''''' is a collaborative work of [[Lisa Gerrard]] 5: with Lisa Gerrard, did not participate in ''Duality''. Pontryagin duality (15626 bytes) 3: ...e theory of [[topological group]]s, '''Pontryagin duality''' explains the general properties of the [[Fouri... 124: One important application of Pontryagin duality is the following characterization of abelian comp... 129: ...ly compact or abelian. One use made of Pontryagin duality between compact abelian groups and discrete abeli... 151: ...) of [[endomorphism]]s in '''LCA''' is changed by duality into its [[dual (category theory)|opposite]] ring... 155: ... in [[category theory]] is called [[Tannaka-Krein duality]]; but this diverges from the connection with [[h... Stone duality (15168 bytes) 1: ...es are usually collected under the label '''Stone duality''', since they form a natural generalization of [... 3: ... article gives pointers to special cases of Stone duality and explains a very general instance thereof in d... 7: ...classically referred to as "Stone duality" is the duality between the category '''Sob''' of [[sober space]]... 19: == Duality of sober spaces and spatial locales == 21: ...p understanding of the concepts of adjunction and duality may well arise from examples such as the result b... Serre duality (3207 bytes) 1: ... this is therefore quite distinct from [[Poincaré duality]], which relates ''H''<sup>''i''</sup> to ''H''<s... 3: ...] determined by the divisor ''D''. That is, Serre duality in this case relates groups ''H''<sup>0</sup>(''D... 15: ...''T'' is the [[tangent bundle]] sheaf ''K''*. The duality shows why these approaches coincide. 17: ...g. While the role of ''K'' above in general Serre duality is played by the [[determinant line bundle]] of t... Duality (projective geometry) (6467 bytes) 1: '''Duality''' in the [[projective plane]] refers to the inte... 43: ...ed. This establishes the bijective nature of the duality in the projective plane. 47: ...to lines. This is analogous to [[dual polyhedron|duality of polyhedra]] in [[solid geometry]], where point... Duality (order theory) (2418 bytes) 3: ... dual order. Formally, this is captured by the '''Duality Principle''' for ordered sets: Particle (661 bytes) Particle accelerator (9281 bytes) Particle (band) (801 bytes) Wino (particle) (342 bytes) Subatomic particle (5599 bytes)
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