Particle Production in Strong Time-dependent Fields

In these lecture notes we give an introduction to the kinetic equation approach to pair production form the vacuum in strong, time-dependent external fields (dynamical Schwinger process). We first give a derivation of the kinetic equation with the source term for the case of fermions starting from the Dirac equation and for bosons from the Klein-Gordon equation. In a second part we discuss the application of the approach to the situation of external field pulses as single-sheeted functions of time (like the Sauter-pulse) and as multi- sheeted functions approximating the situation in the focal point of counter-propagating laser beams. Special emphasis is on the discussion of the time evolution of the system that exhibits the characteristics of a field-induced phase transition for which we discuss the behaviour of the entropy and particle density of the system. We give an outlook to applications of the approach in describing particle production in strong fields formed in particle and nuclear collisions.Comment: 23 pages, 7 figures, Lecture Notes based on arXiv:hep-ph/9809227 and arxiv:1607.08775; to appear in Proceedings of the Helmholtz International Summer School on "Quantum Field Theory at the Limits: From Strong Fields to Heavy Quarks", July 18-30, 2016, Dubna, Russi

On the kinetic equation approach to pair production by time-dependent electric field

We investigate the quantum kinetic approach to pair production from vacuum by time-dependent electric field. Equivalence between this approach and the more familiar S-matrix approach is explicitly established for both scalar and fermion cases. For the particular case of a constant electric field exact solution for kinetic equations is provided and the accuracy of low-density approximation is estimated.Comment: 8 pages, 4 figure

Strange and charm quark-pair production in strong non-Abelian field

We have investigated strange and charm quark-pair production in the early stage of heavy ion collisions. Our kinetic model is based on a Wigner function method for fermion-pair production in strong non-Abelian fields. To describe the overlap of two colliding heavy ions we have applied the time-dependent color field with a pulse-like shape. The calculations have been performed in an SU(2)-color model with finite current quark masses. For strange quark-pair production the obtained results are close to the Schwinger limit, as we expected. For charm quark the large inverse temporal width of the field pulse, instead of the large charm quark mass, determines the efficiency of the quark-pair production. Thus we do not observe the expected suppression of charm quark-pair production connecting to the usual Schwinger-formalism, but our calculation results in a relatively large charm quark yield. This effect appears in Abelian models as well, demonstrating that particle-pair production for fast varying non-Abelian gluon field strongly deviates from the Schwinger limit for charm quark. We display our results on number densities for light, strange, charm quark-pairs, and different suppression factors as the function of characteristic time of acting chromo-electric field.Comment: 6 pages, 2 figures; to appear in the proceedings of the International Conference on Strangeness in Quark matter (SQM2008), Beijing, China, Oct 6-10, 2008; version accepted to J. Phys.