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In physics, a correspondence principle is any one of several premises or assertions about the relationship between classical and quantum mechanics.The physicist Niels Bohr coined the term in 1920 [1] during the early development of quantum theory; he used it to explain how quantized classical orbitals connect to quantum radiation. [2]
Correspondence theory is a traditional model which goes back at least to some of the ancient Greek philosophers such as Plato and Aristotle. [2] [3] This class of theories holds that the truth or the falsity of a representation is determined solely by how it relates to a reality; that is, by whether it accurately describes that reality.
Nevertheless, as explained in the introduction, for states that are highly localized in space, the expected position and momentum will approximately follow classical trajectories, which may be understood as an instance of the correspondence principle. Similarly, we can obtain the instantaneous change in the position expectation value.
In mathematics, the integral of a correspondence is a generalization of the integration of single-valued functions to correspondences. The first notion of the integral of a correspondence is due to Aumann in 1965, [ 1 ] with a different approach by Debreu appearing in 1967. [ 2 ]
Lambek's correspondence is a correspondence of equational theories, abstracting away from dynamics of computation such as beta reduction and term normalization, and is not the expression of a syntactic identity of structures as it is the case for each of Curry's and Howard's correspondences: i.e. the structure of a well-defined morphism in a ...
In theoretical physics, the anti-de Sitter/conformal field theory correspondence (frequently abbreviated as AdS/CFT) is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used in theories of quantum gravity , formulated in terms of string theory or M-theory .
For example, the existence of the (2,0)-theory was used by Witten to give a "physical" explanation for a conjectural relationship in mathematics called the geometric Langlands correspondence. [58] In subsequent work, Witten showed that the (2,0)-theory could be used to understand a concept in mathematics called Khovanov homology . [ 59 ]
A proof of the correspondence theorem can be found here. Similar results hold for rings , modules , vector spaces , and algebras . More generally an analogous result that concerns congruence relations instead of normal subgroups holds for any algebraic structure .