Related papers: One-dimensional relativistic dissipative system wi…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a…
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic…
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
We present a new recipe for relativistic quantum simulation using the first quantisation approach, under periodic (PBC) and Dirichlet (DBC) boundary conditions. The wavefunction is discretised across a finite grid represented by system…
In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to…
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…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. 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…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion.…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We demonstrate that if masses and charges figuring in the equation of motion including both Newton gravitational and Coulomb electrostatic force laws are divided by mass and charge, respectively, which are derived using the relations…