Physics – General Physics
Scientific paper
2011-01-31
Advances in Applied Clifford Algebras, vol. 5, pp. 1-40, (1995)
Physics
General Physics
34 pages? 0 figures. Before the text of the paper there is a comment for physicists, which is important, because the paper has
Scientific paper
The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$, pseudo-vector of the spin $S^{i}$, an action $\hbar \phi $ and a pseudo-scalar $\kappa $. In the quasi-uniform approximation, when all transversal derivatives (orthogonal to the flux vector $j^i$) are small, the system $\mathcal{S}_D$ turns to a statistical ensemble of classical concentrated systems $\mathcal{S}_{dc}$. Under some conditions the classical system $\mathcal{S}_{dc}$ describes a classical pointlike particle moving in a given electromagnetic field. In general, the world line of the particle is a helix, even if the electromagnetic field is absent. Both dynamic systems $\mathcal{S}_D$ and $\mathcal{S}_{dc}$ appear to be non-relativistic in the sense that the dynamic equations written in terms of hydrodynamic variables are not relativistically covariant with respect to them, although all dynamic variables are tensors or pseudo-tensors. They becomes relativistically covariant only after addition of a constant unit timelike vector $f^{i}$ which should be considered as a dynamic variable describing a space-time property. This "constant" variable arises instead of $\gamma $-matrices which are removed by means of zero divizors in the course of the transformation to hydrodynamic variables. It is possible to separate out dynamic variables $\kappa $, $\kappa ^i$ responsible for quantum effects. It means that, setting $\kappa ,\kappa ^i\equiv 0$, the dynamic system $\mathcal{S}_D$ described by the Dirac equation turns to a statistical ensemble $\mathcal{E}_{Dqu}$ of classical dynamic systems $\mathcal{S}_{dc}$.
No associations
LandOfFree
Dirac equation in terms of hydrodynamic variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dirac equation in terms of hydrodynamic variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac equation in terms of hydrodynamic variables will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-647221