Related papers: Towards an Autonomous Formalism for Quantum Mechan…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
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…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a…
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for…
Going back to the early days in the history of quantum mechanics, the interaction of quantum and classical systems stands among the most intriguing open questions in science and makes its appearance in several fields, from physics to…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…