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arXiv:2608.08464

Effect of Strong Field Space-time Features on Vacuum Pair

B. An, N. S. Lin, C. K. Li, M. Jiang, Y. J. Li

quant-phSubmitted Aug 9, 2026• Announced Aug 11, 2026
arXivHTMLPDF

Abstract

The relativistic dynamics of bound states across inertial reference frames are investigated using the computational quantum field theory (CQFT). The results reveal that the spatiotemporal properties of bound states within a given potential well are strictly frame-dependent. Crucially, this spatiotemporal modulation of the external field enables a reduction in the laser intensity threshold required for vacuum electron-positron pair creation. Analytical and numerical calculations demonstrate that this threshold reduction originates from the Lorentz transformation of the four-momentum, which reshapes the vacuum excitation pathways in phase space. By developing CQFT, we establish a comprehensive framework in which relativistic effects intrinsically govern the quantum vacuum decay process

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The relativistic dynamics of bound states across inertial reference frames are investigated using the computational quantum field theory (CQFT). The results reveal that the spatiotemporal properties of bound states within a given potential well are strictly frame-dependent. Crucially, this spatiotemporal modulation of the external field enables a reduction in the laser intensity threshold required for vacuum electron-positron pair creation. Analytical and numerical calculations demonstrate that this threshold reduction originates from the Lorentz transformation of the four-momentum, which reshapes the vacuum excitation pathways in phase space. By developing CQFT, we establish a comprehensive framework in which relativistic effects intrinsically govern the quantum vacuum decay process
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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.
Using space-time resolved solutions in relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum and resolve the Klein-paradox. 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 argue that quantum field theory prohibits the occurrence of Zitterbewegung for an electron in contrast to claims found in textbooks.
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In this chapter, we consider a quantum particle wave function with a bound spectrum of velocity c, and obtain the relativistic momentum based on the group velocity of this wave function. With a space-time isometry condition, the Lorentz transformation and the relativistic dynamics were obtained. Considering a field interacting with a quantum particle as a four-vector conjugated to the space-time vector in the time-dependent phase, we obtain the Lorenz force and the Maxwell equations. It is interesting that only the Ampère-Maxwell equation of a magnetic circuit is specific to the electromagnetic field, while the other equations are general for a field interacting with a charged quantum particle. Considering the time-dependent phase of a quantum particle interacting with an electromagnetic field with a space-time homogeneity condition, we obtain Lorentz transformations for this field. For a quantum particle at a non-relativistic velocity, we obtain a wave function with a very rapidly-varying factor, of a frequency proportional to the rest energy of this particle. From the Schrödinger equation of a particle with a relativistic Hamiltonian, we obtain a split of the wave function into four components, describing a proper rotation of this particle with an angular momentum called spin (Dirac’s relativistic electron theory). Moreover, we also calculate electron potential in the magnetic field, and two-electron interaction potential.