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We developed equations for Wigner functions in strong electromagnetic fields. This allows studying plasma waves and Schwinger pair production, revealing field-strength dependence on particle momentum spread.

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Area of Science:

  • Quantum Field Theory
  • Plasma Physics
  • Strong Field Physics

Background:

  • The behavior of matter under strong electromagnetic fields is crucial for understanding extreme physical conditions.
  • The Wigner function offers a phase-space description of quantum systems, useful for analyzing field interactions.

Purpose of the Study:

  • To derive a system of coupled partial differential equations for the equal-time Wigner function in strong electromagnetic fields.
  • To analyze plasma wave propagation and Schwinger pair production in the electrostatic limit.

Main Methods:

  • Utilized the Dirac-Heisenberg-Wigner formalism to derive the Wigner function equations.
  • Applied Ampère's law and the local density approximation for specific case studies.
  • Derived dispersion relations for wave propagation and analyzed pair production rates.

Main Results:

  • A system of four coupled partial differential equations for the Wigner function in the electrostatic limit was obtained.
  • Investigated linearized wave propagation in plasma, including nonzero vacuum expectation values, and derived the dispersion relation.
  • Studied Schwinger pair production, finding its rate's dependence on perpendicular momentum is influenced by the electric field strength.

Conclusions:

  • The derived formalism provides a framework for studying quantum systems in strong electromagnetic fields.
  • The results offer insights into plasma dynamics and particle creation mechanisms under extreme conditions.
  • The perpendicular momentum spread of produced pairs is sensitive to the applied electric field strength.