Related papers: Discrete Spacetime and Relativistic Quantum Partic…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that…
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity, because the allowed quantum states must obey the Hamiltonian constraint. (ii) During…
The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve.…
We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times. In previous work, two of us have proposed a "minimal subtraction" prescription for…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
In this paper, we investigate the spacetime containing both small-scale structures (wiggles) and spatial dislocation, forming a wiggly cosmic dislocation. We study the combined effects of these features on the dynamics of massive and…
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees…
The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic.…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
We regard the background of space-time as a physical system composed of discrete volume elements at the Planck scale and get the internal energy of space-time by Debye model. A temperature-dependent minimum energy limit of the particles is…
Noticing that really the fermions of the Standard Model are best thought of as Weyl - rather than Dirac - particles (relative to fundamental scales located at some presumably very high energies) it becomes interesting that the experimental…
A short review of special relativistic dynamics describing a particle acted upon by an arbitrary conservative external force is presented. If the mass of the particle is zero and the force is central then the equations of motion turn out to…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…