Relativistic Electron Localization and the Lack ofZitterbewegung

Abstract

Using space-time resolved solutions to relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum. For early times the entangled electron-positron wave function can be obtained analytically. We show that there are, in principle, no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also find that quantum field theory prohibits the occurrence of Zitterbewegung for an electron.

Propagation of a relativistic electron wave packet in the Dirac equation

“…Here, spinor coefficients u ± i are expressed more conveniently with γ using Eq. (10). Figure 1 shows the p dependence of spinor vectors.…”

“…The Zitterbewegung is often presented as if it refers to an observable trembling motion associated with a real physical particle [6,7]; for example, it was suggested as the origin of the electron spin [8], and it is given as a reasoning for the Darwin term [9] in atomic fine structure. However, this concept is controversial and was challenged by Krekora et al [10]. The existence of Zitterbewegung, in relativistic quantum mechanics and in quantum field theory, has been a recurrent subject of discussion over the past years [10][11][12].…”

“…However, this concept is controversial and was challenged by Krekora et al [10]. The existence of Zitterbewegung, in relativistic quantum mechanics and in quantum field theory, has been a recurrent subject of discussion over the past years [10][11][12]. The interest in Zitterbewegung was recently rekindled due to its analog in Dirac-like systems [13][14][15][16][17][18].…”

Zitterbewegung in Bogoliubov's System

“…On the other hand, in the quantum field theory which allows particles (and antiparticles) to be temporarily created and annihilated by satisfying Heisenberg's uncertainty principle, one could interpret the ZB as the resulting effect of successive scattering between an original electron and virtual electron-positron pairs (i.e. the process of quantum vacuum polarization) [8][9][10]. Different relativistic quantum theories give distinct explanations of the ZB, be that as it may, it is fairly a reasonable perspective that the ZB should be present in a great number of * Electronic address: flzhang@tju.edu.cn † Electronic address: chenjl@nankai.edu.cn physical systems [11], possibly including those in which the electron could be in a bound state.…”

Electron-positron pair creation induced by quantum-mechanical tunneling

“…It can provide an alternative approach to the traditional S-matrix approach, which is based on the in-and out-states only and therefore cannot visualize the processes inside the interaction zone. In addition to visualizing the details of the pair creation dynamics, direct time-dependent quantum field theoretical solutions to the Dirac equation have also contributed to the resolution of various conceptual problems related to the negative energy states such as the Zitterbewegung [23], the relativistic localization problem [24] as well as the Klein-paradox [25][26][27][28].…”