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Metaplectic group

In mathematics and mathematical physics, the metaplectic group is the group that describes how the basic symmetries of classical mechanics act in quantum mechanics. More precisely, the symplectic group consists of the linear changes of position and momentum that preserve the form of Hamiltonian mechanics; equivalently, it is the group of canonical…

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Overview

Motivation from quantum mechanics

Definition

Explicit construction for n = 1

Construction of the Weil representation

Generalizations

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Metaplectic group

Nodes62
Edges61
Triples29
Avg. degree1.97
Density0.032258
Components1

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Metaplectic group

Top relations

related to Generalizations · 8
Metaplectic group → Heisenberg, L2, Pontryagin, Some, The, The Hilbert, There, Weil
related to Definition · 7
Metaplectic group → It, Lie, Mp2n, Sp2n, The, Therefore, Weil
related to External links · 7
Metaplectic group → American Mathematical Society, Martin, May, Notices, PDF, Weissman, What
related to Motivation from quantum mechanics · 5
Metaplectic group → After, For, Hamiltonian, In, One
is a · 2
Metaplectic group → group that describes how the basic symmetries of classical mechanics act in quantum mechanics, version of this idea associated with symplectic geometry and canonical transformations rather than with Euclidean rotations

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Important terminology

group metaplectic symplectic displaystyle representation cover weil space double canonical case multiplication functions linear transformations mechanics action heisenberg mathcal one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Metaplectic groupis agroup that describes how the basic symmetries of classical mechanics act in quantum mechanics0.90text
Metaplectic groupis aversion of this idea associated with symplectic geometry and canonical transformations rather than with Euclidean rotations0.90text
Metaplectic grouprelated to DefinitionThe0.60section
Metaplectic grouprelated to DefinitionLie0.60section
Metaplectic grouprelated to DefinitionSp2n0.60section
Metaplectic grouprelated to DefinitionMp2n0.60section
Metaplectic grouprelated to DefinitionTherefore0.60section
Metaplectic grouprelated to DefinitionIt0.60section
Metaplectic grouprelated to DefinitionWeil0.60section
Metaplectic grouprelated to External linksWeissman0.60section
Metaplectic grouprelated to External linksMartin0.60section
Metaplectic grouprelated to External linksMay0.60section

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