Related papers: Dynamics of Totally Constrained Systems I. Classic…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is studied. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics that of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and…
The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
During the last three decades, P. B\'{o}na has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence of…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…