Related papers: On the geometry of quantum constrained systems
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
In orthodox quantum theory the observables of spacelike separated quantum systems commute. I shall call this the commutation constraint. It severely limits quantum theory's explanatory power. For instance, the constraint cannot be met in…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
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…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…