Production of partons in the presence of classical fields in ultrarelativistic heavy-ion collisions

In this work the production of quarks, antiquarks and of gluonic fluctuations is studied in the presence of classical bosonic field. A comparison of the production of anti-quark pairs with the creation of pairs of gluonic quantum fluctuations based on perturbative calculations will be presented here. This analysis is valid for quantum particles with a large momentum compared to the magnitude of the classical vector potential multiplied by the coupling constant. The model contains 3 parameters: the initial magnitude of the gauge field, the coupling constant and the time scale on which the field decays. It appears that none of the species (quark-antiquark pairs, gluonic fluctuation pairs, bosons and fermion-anti fermions) can be neglected from the beginning. A corresponding calculation requires a non-perturbative description of at least the soft fermions. In this thesis the exact expression for fields varying arbitrarily in time is derived. After the full solution has been obtained, various approximation schemes are proposed for different domains, in order to find out into which the situation under consideration falls. There are approximations in the ultraviolet (perturbative), the infrared, and the Abelian (commutative) regime. The exact expression and the lowest orders of the different approximation schemes are evaluated in the presence of the model field with the same parameters as before. (A.C.)