Initial value problem for plasma oscillations

1991 ◽  
Vol 3 (5) ◽  
pp. 1158-1166 ◽  
Author(s):  
Jin Li ◽  
Günther Otto Spies
Keyword(s):  
Initial Value Problem ◽  
Initial Value ◽  
Plasma Oscillations

scholarly journals PAIR PRODUCTION IN A STRONG ELECTRIC FIELD: AN INITIAL VALUE PROBLEM IN QUANTUM FIELD THEORY

1993 ◽  
Vol 02 (02) ◽  
pp. 333-380 ◽  
Author(s):  
Y. KLUGER ◽  
J.M. EISENBERG ◽  
B. SVETITSKY
Keyword(s):  
Field Theory ◽  
Electric Field ◽  
Initial Value Problem ◽  
Particle Creation ◽  
Mean Field Approximation ◽  
Time Behavior ◽  
Initial Value ◽  
Plasma Oscillations ◽  
Physical Features ◽  
Creation Rate

We review recent achievements in the solution of the initial-value problem for quantum backreaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining backreaction has to do with applications to theoretical models of production of the quark-gluon plasma though we here address practicable solutions for backreaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features like plasma oscillations and plateaus in the current appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.

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