相关论文: Time as an operator/observable in nonrelativistic …

Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…

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…

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint $4\times 4$ relativistic time operator for…

The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…

This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the…

In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…

A model of discrete space-time is presented which is, in a sense, both Lorentz invariant and has no restriction on the relative velocity between particles (except v < c). The space-time has an inbuilt indeterminacy. Published originally as…

In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product…

Time it takes to travel from one position to another, devoid of any quantum mechanical description, has been modeled variously, especially for quantum tunneling. The model time, if universally valid, must be subluminal, must hold everywhere…

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…

The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…

The phenomenon of local dynamical inhomogeneity of time is predicted, which implies that the course of time along the trajectory of motion of a particle in the inertial reference frames moving relative to each other depends on the state of…

Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…

Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames (RF) quantum effects is considered in Relativistic Quantum Mechanics framework. For RF connected with some macroscopic object its free quantum motion - wave…

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…

The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…

We analyze relativistic quantum scattering in the Schr\"odinger picture. The suggestive requirement of translational invariance and conservation of the four-momentum, that the interacting Hamiltonian commute with the four-momentum $P$ of…