On the notion of phase in mechanics

Abstract

The notion of phase plays an esential role in both classical and quantum mechanics.But what is a phase? We show that if we define the notion of phase in phase (!) space one can very easily and naturally recover the Heisenberg-Weyl formalism; this is achieved using the properties of the Poincare-Cartan invariant, and without making any quantum assumption.

References in corpus (1)

• The "Symplectic Camel Principle" and Semiclassical Mechanics

Cited by in corpus (6)

• Evolution of hybrid quantum-classical wavefunctions
• Hybrid quantum-classical dynamics of pure-dephasing systems
• Extended Weyl Calculus and Application to the Phase-Space Schrödinger Equation
• Koopman wavefunctions and Clebsch variables in Vlasov-Maxwell kinetic theory
• Hénon-Heiles Interaction for Hydrogen Atom in Phase Space
• Generalised Geometric Phase