The concept of Diff 4 invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of S-matrix at quantum level. In this paper the possibility of identifying Diff 4 invariant Poincare transformations as the recently discovered Lorentz invariant d...

It is well known that the Galilei algebra is a sub algebra of Poincare algebra in one space dimension more. 1 This fact allows us to relate relativistic Poincare and Galilean theories. An interesting point is that Galilei transformations in two space dimensions are contained in the usual Poincare transformations? This enables us to present Poincare spin zero wavefunctions as Fourier transforms ...

There are Poincare group representations on complex Hilbert spaces, like the Dirac spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. The Majorana-Fourier and Majorana-Hankel transforms of Majo...

The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentumvector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different values of θ for the θ-term in QCD lagrangian lead to different representations of the Poincare group, which are, however, connected by an unitary transformation...

We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180 degrees and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fix...

The head-neck system has multiple degrees of freedom in both its control and response characteristics, but is often modeled as a single joint mechanical system. In this study, we have attempted to quantify the perturbation parameters that would elicit nonlinear responses in a single degree-of-freedom neuromechanical system at small amplitudes and velocities of perturbation. Twelve healthy young...

In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincare maps of the flow observed in Khakhar et al. is resolved. It is shown that in long...

A model potential for two-particle relativistic systems is investigated in the framework of Poincare-invariant quantum mechanics (or relativistic Hamiltonian dynamics). The potential considered allows to reduce the main integro-differential equation of Poincare-invariant quantum mechanics to the equation analogous to the radial equation and have analytical solution for relativistic bound system...