A real version of the Dirac equation is derived and its coupling to the electromagnetic field considered. First the four-component real Majorana equation is briefly discussed. Then the complex Dirac equation including...A real version of the Dirac equation is derived and its coupling to the electromagnetic field considered. First the four-component real Majorana equation is briefly discussed. Then the complex Dirac equation including an electromagnetic field will be written as an eight-component real spinor equation by separating it into its real and imaginary parts. Through this decomposition, what becomes obvious is the way in which the electromagnetic field couples to charged fermions (electron and positron) when being described by real spinor fields. Thus, contrary to common expectation, charged fermions can also be described by a real Dirac equation if they are considered as a doublet related to the SO(2) symmetry group, which enables a matrix coupling to the electromagnetic field and corresponds to the usual U(1) gauge symmetry of the standard Dirac equation.展开更多
Scientists have traditionally employed superimposed mutually-coherent electron beams for holography and phase retrieval of electron wavepackets.However,recent theoretical exploration delves into the interaction of sup...Scientists have traditionally employed superimposed mutually-coherent electron beams for holography and phase retrieval of electron wavepackets.However,recent theoretical exploration delves into the interaction of superposed electron beams with the matter.This investigation aims to elucidate long-range Coulomb correlations and quantum decoherence phenomena when electrons interact with their environment.展开更多
We identified 28 discrete electron events(DEEs) with enhanced fluxes at ~50-200 keV in the high-altitude cusp/polar cap/lobe,using the electron measurements by the BeiDa Image Electron Spectrometer(BD-IES) instrument ...We identified 28 discrete electron events(DEEs) with enhanced fluxes at ~50-200 keV in the high-altitude cusp/polar cap/lobe,using the electron measurements by the BeiDa Image Electron Spectrometer(BD-IES) instrument onboard an inclined(55°)geosynchronous orbit(IGSO) satellite from October 2015 to January 2016. We find that among the 28 DEEs, 22 occur in the nightside and mostly in the northern cusp/polar cap/lobe, while 6 occur in the dayside and all in the southern cusp; 24 events correspond to an average interplanetary magnetic field(IMF) component B_z>0, 3 correspond to an average IMF B_z<0, and 1 has no OMNI IMF data. In these DEEs, the observed average omnidirectional electron differential flux generally fits well to a power-law spectrum, J^E^(-γ), with the spectral index y ranging from 2.6 to 4.6, while the average electron flux varies over three orders of magnitude from event to event. The spectral index of these cusp DEEs are(strongly) larger than the spectral index of solar wind superhalo electrons(radiation belt electrons) observed by the WIND 3 D Plasma & Energetic Particle instrument(the BD-IES). At^110 keV,the electron flux of DEEs in the cusp/polar cap/lobe shows a weak positive correlation with the solar wind superhalo electron flux but no obvious correlation with the radiation belt electron flux. These results suggest that these DEEs probably originate from transient processes acting on the solar wind superhalo electrons, e.g., the mid/high-latitude reconnection.展开更多
Stimulated and spontaneous interactions of electron wavepackets with optical near fields were explored with complementary techniques.In striking agreement with theory,scientists have demonstrated the dependence of spo...Stimulated and spontaneous interactions of electron wavepackets with optical near fields were explored with complementary techniques.In striking agreement with theory,scientists have demonstrated the dependence of spontaneous and stimulated quantum mechanical processes on the spatial distribution of optical modes.展开更多
文摘A real version of the Dirac equation is derived and its coupling to the electromagnetic field considered. First the four-component real Majorana equation is briefly discussed. Then the complex Dirac equation including an electromagnetic field will be written as an eight-component real spinor equation by separating it into its real and imaginary parts. Through this decomposition, what becomes obvious is the way in which the electromagnetic field couples to charged fermions (electron and positron) when being described by real spinor fields. Thus, contrary to common expectation, charged fermions can also be described by a real Dirac equation if they are considered as a doublet related to the SO(2) symmetry group, which enables a matrix coupling to the electromagnetic field and corresponds to the usual U(1) gauge symmetry of the standard Dirac equation.
文摘Scientists have traditionally employed superimposed mutually-coherent electron beams for holography and phase retrieval of electron wavepackets.However,recent theoretical exploration delves into the interaction of superposed electron beams with the matter.This investigation aims to elucidate long-range Coulomb correlations and quantum decoherence phenomena when electrons interact with their environment.
基金supported by the National Natural Science Foundation of China(Grant Nos.41421003,41474148,41774183&41374167)Major Project of Chinese National Programs for Fundamental Research and Development(Grant No.2012CB825603)
文摘We identified 28 discrete electron events(DEEs) with enhanced fluxes at ~50-200 keV in the high-altitude cusp/polar cap/lobe,using the electron measurements by the BeiDa Image Electron Spectrometer(BD-IES) instrument onboard an inclined(55°)geosynchronous orbit(IGSO) satellite from October 2015 to January 2016. We find that among the 28 DEEs, 22 occur in the nightside and mostly in the northern cusp/polar cap/lobe, while 6 occur in the dayside and all in the southern cusp; 24 events correspond to an average interplanetary magnetic field(IMF) component B_z>0, 3 correspond to an average IMF B_z<0, and 1 has no OMNI IMF data. In these DEEs, the observed average omnidirectional electron differential flux generally fits well to a power-law spectrum, J^E^(-γ), with the spectral index y ranging from 2.6 to 4.6, while the average electron flux varies over three orders of magnitude from event to event. The spectral index of these cusp DEEs are(strongly) larger than the spectral index of solar wind superhalo electrons(radiation belt electrons) observed by the WIND 3 D Plasma & Energetic Particle instrument(the BD-IES). At^110 keV,the electron flux of DEEs in the cusp/polar cap/lobe shows a weak positive correlation with the solar wind superhalo electron flux but no obvious correlation with the radiation belt electron flux. These results suggest that these DEEs probably originate from transient processes acting on the solar wind superhalo electrons, e.g., the mid/high-latitude reconnection.
文摘Stimulated and spontaneous interactions of electron wavepackets with optical near fields were explored with complementary techniques.In striking agreement with theory,scientists have demonstrated the dependence of spontaneous and stimulated quantum mechanical processes on the spatial distribution of optical modes.
