Related papers: Quantum Mechanics for Totally Constrained Dynamica…
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally…
This work concerns a new reformulation of quantum geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
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…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…