Constrained Hamiltonian formalism for unconstrained classical mechanics

Hamiltonian Formalism in Quantum Mechanics

To Vladimir Igorevich Arnol'd with admiration, on occasion of his 60 th birthday. Abstract Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their propert...

Projection formalism for constrained dynamical systems: from Newtonian to Hamiltonian mechanics.

The Hamiltonian of a holonomically constrained dynamical many-particle system in Cartesian coordinates has been recently derived for applications in statistical mechanics [G. R. Kneller, J. Chem. Phys. 125, 114107 (2006)]. Using the same projector formalism, we show here the equivalence of the corresponding equations of motion with those obtained from a Newtonian and a Lagrangian description. I...

Lagrangian and Hamiltonian Formalism for Constrained Variational Problems

We consider solutions of Lagrangian variational problems with linear constraints on the derivative. These solutions are given by curves γ in a differentiable manifold M that are everywhere tangent to a smooth distribution D on M ; such curves are called horizontal. We study the manifold structure of the set ΩP,Q(M,D) of horizontal curves that join two submanifolds P and Q of M . We consider an ...

Complex Variables in Classical Hamiltonian Mechanics

Autonomous geometro-statistical formalism for quantum mechanics I : Noncommutative symplectic geometry and Hamiltonian mechanics

Considering the problem of autonomous development of quantum mechanics in the broader context of solution of Hilbert's sixth problem (which relates to joint axiomatization of physics and probability theory), a formalism is evolved in this two-part work which facilitates the desired autonomous development and satisfactory treatments of quantum-classical correspondence and quantum measurements. T...