Related papers: Quantum mechanics on York slices
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and…
We study cosmological perturbation theory with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a matter-time gauge. The corresponding canonical action describes the dynamics of the scalar…
We examine in greater detail the proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants, a situation often found in "relational time" settings. We show in detail…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…
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…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
We develop a systematic classical framework to accommodate canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…
An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as…