Dynamics of Totally Constrained Systems. II: Quantum Theory

Dynamics of Totally Constrained Systems II . Quantum Theory

In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a relative probability amplitude functional Ψ which determines the relative probability for each state to be observed, instead of on the state vectors as in the ...

Dynamics of Totally Constrained Systems I. Classical Theory

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints hα with arbitrary coefficients. The main purpose of the present paper is to make clear that classical dynamics of a totally constrained system is nothing but the fo...

Effective Dynamics for Constrained Quantum Systems

We consider the time dependent Schrödinger equation on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When we scale the potential in the directions normal to C by a parameter ε 1, the solutions concentrate in an ε-neighborhood of the submanifold. We derive an effective Schrödinger equation on the submani...

Quantum Mechanics for Totally Constrained Dynamical Systems and Evolving Hilbert Spaces

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a generalization of the usual procedure of deparametrization of relational theories with hamiltonian constraint that allow to include systems with an evolving Hi...

Constrained Multivariable Operator Theory Ii