# Duality

Also found in: Dictionary, Thesaurus, Financial, Wikipedia.

## Duality (physics)

The state of having two natures, which is often applied in physics. The classic example is wave-particle duality. The elementary constituents of nature—electrons, quarks, photons, gravitons, and so on—behave in some respects like particles and in others like waves.

Duality is often used in a more precise sense. It indicates that two seemingly different, theoretical descriptions of a physical system are actually mathematically equivalent. Such an occurrence is very useful. Various properties and phenomena are clearer in one or the other of the descriptions, and calculations that are difficult or impossible in one description may be simple in the other. In the case of wave-particle duality, the wave description corresponds to a theory of quantized fields, where the field variables are governed by an uncertainty principle. The particle description corresponds to a Feynman integral over all particle paths in spacetime. The quantized-field and path integral theories sound very different but are mathematically equivalent, making identical predictions. See Feynman integral, Quantum field theory, Quantum mechanics, Uncertainty principle, Wave mechanics

#### Weak-strong duality

In some systems, there is weak-strong duality, meaning that when the coupling constant g of the original description is large that of the dual description, g, is small; for example g = 1/g. When g is large, so the interactions in the original description are strong and the perturbation theory in this description is highly inaccurate, then perturbation theory in the dual description gives a very accurate description.

#### Duality in superstring theory

It is believed that a complete theory of all particles and interactions must be based on quantization of one-dimensional objects (loops) rather than points: this is superstring theory. In superstring theory there is again the problem that perturbation theory is the main tool, giving an incomplete description of the physics. The situation has greatly improved with the discovery that weak-strong duality is a general property of string theory. In fact, there are five known string theories, and all are dual to one another. A notable feature in string theory is that in addition to strings and solitons, duality requires certain other objects as well: D-branes, which are local disturbances to which strings become fixed. Remarkably, the same methods have also been used to solve some long-standing problems regarding the quantum mechanics of black holes. See Quantum gravitation;, Superstring theory

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
"As a provider of a data science platform optimized for homomorphic encryption, we are excited to be working with Intel and Microsoft Research on this industry standardization initiative," said Kurt Rohloff, CTO and co-founder of Duality Technologies and associate professor, New Jersey Institute of Technology.
The research concluded that on the econometric level, no impact of CEO duality had been found of organizational performance, but when researchers checked the industry wise impact, it has been found that CEO duality affects the organizational performance.
Five decades after the adoption of the Official Languages Act, and more than 30 years after the enshrinement of linguistic duality in the Canadian Charter of Rights and Freedoms, language continues to be contentious.
These variables proxy the following key policy objectives of Abenomics, respectively: i) achieving positive inflation in a stable manner; ii) increasing flexibility in the labor market and reducing duality; iii) increasing the female labor participation rate; and iv) increasing overall labor input.
The duality is carried throughout all of the branding, with all of the shade names in Spanish and the product names in English.
In total, the visual, comprehensive wheel of duality presented herein logically connects 14 interconnected microeconomic concepts, and outlines how one can make 16 microeconomically logical transitions among the aforementioned dual and demand functions, which are commonly discussed and applied in the context of duality in consumer theory.
Sufficient optimality conditions and Mond-Weir duality theorems are derived by the assumption of generalized nonsmooth ([phi], [rho])-invexity between Banach spaces.
Keywords Climate change * Institutional duality * Institutional theory * Subsidiaries
SMSE duality [20] is useful to transceiver design for single relay multi-user (SRMU) MIMO network.
Professor Spinelli's proposition of a 'both/and' duality opened up the possibility for me to integrate the relative impact of childhood deficits whilst viewing the individual from a broader existential-phenomenological perspective.
There is a (partial) duality between strict convexity and smoothness given by the following Klee's theorem (see [8, Chapter 2, [section]1, Theorem 2]):

Site: Follow: Share:
Open / Close