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Electric current from Schwinger's time-ordered propagator

Cristian Villavicencio

Abstract

The quasistatic electric current density of fermions in the presence of an external electric field is determined through the utilization of a time-ordered Schwinger propagator. The study encompasses the necessary conditions for establishing a well-defined time-ordered propagator within the Schwinger formalism, specifically concentrating on constant and uniform electromagnetic fields. Within this theoretical framework, a chemical potential is introduced, resulting in non-zero values for the electric current and charge number density. Consequently, the dependence of electric conductivity on the strength of the electric field and the charge number density is investigated.

Electric current from Schwinger's time-ordered propagator

Abstract

The quasistatic electric current density of fermions in the presence of an external electric field is determined through the utilization of a time-ordered Schwinger propagator. The study encompasses the necessary conditions for establishing a well-defined time-ordered propagator within the Schwinger formalism, specifically concentrating on constant and uniform electromagnetic fields. Within this theoretical framework, a chemical potential is introduced, resulting in non-zero values for the electric current and charge number density. Consequently, the dependence of electric conductivity on the strength of the electric field and the charge number density is investigated.
Paper Structure (6 sections, 31 equations, 2 figures)

This paper contains 6 sections, 31 equations, 2 figures.

Table of Contents

  1. Time ordered propagator
  2. Schwinger's Green function regularization
  3. Electric field
  4. Electric current and charge number density
  5. Results
  6. Conclusions

Figures (2)

  • Figure 1: Electric conductivity normalized by $mq^2$ as a function of the external electric field number in units of the fermion mass for different values of the charge density.
  • Figure 2: Electric conductivity normalized by $mq^2$ as a function of the number charge density in units of the fermion mass for different values of the external electric field.