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--- advanced_tools:group_theory:representation_theory:metaplectic_representation [2017/07/04 09:18]
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+++ advanced_tools:group_theory:representation_theory:metaplectic_representation [2018/04/08 16:14] (current)
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 knowledge of the wave function. Both classical and quantum motion are
 thus deduced from the same mathematical object, the Hamiltonian flow.
+[...]
+We will in fact see that both classical and quantum mechanics rely on
+the same mathematical object, the [[formalisms:hamiltonian_formalism|Hamiltonian flow]], viewed as an abstract
+group. If one makes that group act on points in phase space, via its symplectic representation, one obtains Hamiltonian mechanics. If one makes it
+act on functions, via the metaplectic representation, one obtains quantum
+mechanics. It is remarkable that in both cases, we have an associated theory of motion: in the symplectic representation, that motion is governed
+by Hamilton’s equations.
 <cite>chapter 6 and 7 in The Principles of Newtonian and Quantum Mechanics by M. Gosson</cite>