Stochastic Conservation Laws?

We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created fluctuationally from a background Zero Point Field. We conclude that these conservation laws are to be taken in the spirit of thermodynamic laws.Comment: 5 pages, Te

Deriving Spin within a discrete-time theory

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called "Non-Newtonian Mechanics"). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.'s formulation).Comment: 10 pages; LaTeX fil

Minimal coupling method and the dissipative scalar field theory

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative system investigated. Some kinematical relations calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment obtained.Comment: 15 pages, no figur

On the Classical Theory of the Electron

A classical theory of the electron, proposed by one of us several years ago and based on finite-difference equations, is discussed by considering the three possible following cases: radiating electron, absorbing electron and nonradiating, nonabsorbing electron. In particular the so-called transmission laws necessary to determine, in conjunction with the dynamical equations, the motion of a charged particle corresponding to given initial values of position and velocity are critically reconsidered. The general characteristics of the one-dimensional motion in the non-relativistic approximation are discussed in detail. It is found that in the case of the radiating electron the particle position tends asimptotically to the point of stable equilibrium. The present theory is, therefore, free from the unphysical phenomenon of runaway solutions. These general results are illustrated by studying the motion of a particle under the action of a restoring elastic force and under the action of purely time-dependent forces

A Canonical Approach to the Quantization of the Damped Harmonic Oscillator

We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem, characterising both forward and backward time propagations are given. A Hamiltonian analysis, showing the equivalence with the Lagrangian approach, is also done. Based on this Hamiltonian analysis, the quantization of the model is discussed.Comment: Revtex, 6 pages, considerably expanded with modified title and refs.; To appear in J.Phys.

The Fractal Universe

In this talk, we touch upon the chaotic and fractal aspects of the Universe.Comment: 5 pages, Te

Comments on discrete time in quantum mechanics

The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation

Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U_0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. For both the linear and the exponential barrier we provide an explicit formula for the delay time \tau(E) as a function of the peak energy E. We display the resonant behavior of \tau(E) at energies close to U_0. By analyzing the asymptotic behavior for large energies of the eigenfunctions of the continuous spectrum we also show that, as expected, \tau(E) approaches the classical value for E -> \infty, thus diverging for the step-linear case and vanishing for the step-exponential one.Comment: 14 pages, 10 figure