狄拉克（Dirac）与当代物理学

Yuri A. Rylov

Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor. In the first case the Dirac equation is nonrelativistic, in the second one it is relativistic. Transforming Dirac equation to another scalar-vector variables, one shows that the first way of transformation is valid, and the Dirac equation is not relativistic

Takashi Ichinose

F. Masafumi Toyama, Yukihisa Nogami, Francisco Antônio Bezerra Coutinho

The behaviour of wavepackets of the `Dirac oscillator' in (1 + 1) dimensions is examined. The Dirac oscillator is a relativistic extension of the harmonic oscillator. We construct a wavepacket in the usual Dirac representation and another one in the Foldy - Wouthuysen (FW) representation. In the nonrelativistic limit, these wavepackets are both reduced to Schrödinger's coherent wavepacket for the harmonic oscillator. The wavepacket in the Dirac representation exhibits Zitterbewegung whereas the one in the FW representation does not. We find that the wavepacket in the FW representation behaves much more like a classical particle than that of the Dirac representation. This gives insights into Ehrenfest's theorem for the Dirac equation.

俊之助 武藤, 井上 謙藏

Tudor Stefan Ratiu, Oleg Georgievich Smolyanov

This paper describes the states of quantum versions of finite dimensional Hamilton–Dirac systems in terms of (analogues of) the Wigner function (various definitions of Wigner functions for classical Hamiltonian systems can be found in [8]). We give a system of equations, which we call the Moyal–Dirac system, describing the evolution of this Wigner function. The passage from the Moyal equation describing the evolution of the quantum version of a classical Hamiltonian system to the Moyal–Dirac system describing the evolution of the quantum version of the corresponding Hamilton–Dirac system is similar to the passage from the Liouville equation describing the evolution of a classical Hamiltonian system to the Liouville–Dirac system of equations describing the evolution of the corresponding Hamilton–Dirac system. Thus, our Moyal–Dirac system is a generalization of both the Liouville–Dirac system and the Moyal equation