How Dirac Fields operate part1(Particle Physics)
- de Broglie-Bohm formulation of Dirac fields(arXiv)
Author : Luca Fabbri
Abstract : We present the theory of Dirac spinors in the formulation given by Bohm on the idea of de Broglie: the quantum relativistic matter field is equivalently re-written as a special type of classical fluid and in this formulation it is shown how a relativistic environment can host the non-local aspects of the above-mentioned hidden-variables theory. Sketches for extensions are given at last.
2. New symmetries, conserved quantities and gauge nature of a free Dirac field(arXiv)
Author : Vladimir V. Kassandrov, Nina V. Markova
Abstract : We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein-Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or string-like singularities) can be obtained via differentiation of a corresponding pair of the KGE solutions for a doublet of scalar fields. On this way we obtain a “spinor analogue” of the mesonic Yukawa potential and previously unknown chains of solutions to DE and KGE, as well as an exceptional solution to the KGE and DE with a finite value of the field charge (“localized” de Broglie wave). The pair of scalar “potentials” is defined up to a gauge transformation under which corresponding solution of the DE remains invariant. Under transformations of Lorentz group, canonical spinor transformations form only a subclass of a more general class of transformations of the solutions to DE upon which the generating scalar potentials undergo transformations of internal symmetry intermixing their components. Under continious turn by one complete revolution the transforming solutions, as a rule, return back to their initial values (“spinor two-valuedness” is absent). With arbitrary solution of the DE one can associate, apart of the standard one, a non-canonical set of conserved quantities, positive definite “energy” density among them, and with any KGE solution — positive definite “probability density”, etc. Finally, we discuss a generalization of the proposed procedure to the case when the external electromagnetic field is present
3.Traveling Wave Form Description for Dirac Field and Its Deduction To Pauli Equation Type Forms in Quantum Mechanics (arXiv)
Author : Fei Wang
Abstract : We derive an equivalent traveling wave form description for Dirac field. In the non-relativistic limit, such form can reduce to inverse-Galilean transformed Schrodinger-type equation. We find that, the resulting two-component Schrodinger-type equation from the reduction of traveling wave form description of Dirac field is different to the naive Galilean transformed Schrodinger equation. Taking into account the interactions of the system to electromagnetic field by adding proper forms of covariant derivative, the traveling wave form description for Pauli equation can be similarly obtained in the non-relativistic limit. Such descriptions allow one to choose arbitrary convenient reference frame for quantum system involving spins. Using Bargmann-Wigner formalism for field with arbitrary spin s≥1/2, which satisfy Dirac-type equations in all its indices, the traveling wave description for such a field can be similarly obtained from the traveling wave form description of Dirac field, for example, for the spin-3/2 Rarita-Schwinger field and spin-2 gravitational field.
