Quantum Mechanics of Dirac Particles

Garnet N. Ord

Yuri A. Rylov

The Dirac particle S_D is investigated by means of dynamic methods, i.e. without a use of the principles of quantum mechanics. It is shown that the Pauli particle S_P and the nonrelativistic approximation S_{nD} of the Dirac particle S_D are different dynamic systems. S_{nD} contains the high frequency degrees of freedom, which are absent in the dynamic system S_P. It means that the nonrelativistic Dirac particle S_{nD} is composite (i.e. it has internal degrees of freedom), whereas the Pauli particle S_P is a pointlike particle with the spin. In the absence of the electromagnetic field the world line of the classical Pauli particle S_{Pcl} is a timelike straight, whereas that of the classical nonrelativistic Dirac particle S_{nDcl} is a helix. The characteristic frequency $Ω=2mc^{2}/\hbar $ of this helix is the threshold frequency of the pair production. Using dynamic methods, one shows freely that the Copenhagen interpretation, when the wave function is a specific quantum object describing the state of individual particle, is incompatible with the quantum mechanics formalism. Besides, it is shown that the momentum distribution in quantum mechanics is in reality the mean momentum distribution. Effectiveness of different investigation strategies is discussed and compared.

Boris N. Chichkov

The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation corresponding to the energy conservation equation of Einstein's special relativity. First, scalar quantum mechanics of particles operating with their wave functions is discussed. Using the first quantization of the photon-like dispersion relation, very simple new derivation of the Dirac equation is given. Then, vector field quantum mechanics is introduced, which defines vector fields associated with the relativistic particle. Basic equations for the vector-field quantum mechanics, similar to the source-free Maxwell equations, are derived. Following these equations, the particle's de Broglie wave can be considered as the transversal electromagnetic wave. Therefore, the wave-particle duality can be redefined as the electromagnetic wave-particle duality. Relationships between the scalar and vector field quantum mechanics are analyzed.

Vilas Y. Rajopadhye

Lucas Lamata, Jorge Casanova, R. Gerritsma +3 more

We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.