Non-Perturbative Quantum Field Theory in Extreme Environments

Abstract: The aim of this thesis is to describe some physical systems which can be treated by non-perturbative methods in quantum field theory. In the thesis we study systems described by quadratic Hamiltonians, possibly extended with an external electromagnetic field and/or with a thermal heat bath. We also study the (mass less) Schwinger model and boson stars. Apart from the Schwinger model, the systems all have extreme environments. For example, electric field strengths of 1016 V/cm and magnetic field strengths of 109 T as well as temperatures of 109 K are considered.

A good conceptual basis for non-perturbative methods in quantum field theory is the functional Schrödinger representation. It is also well-suited for discussing equilibrium as well as out-of-equilibrium statistical mechanics in quantum field theory by means of density matrices. In the thesis we review and develop the functional Schrödinger representation and introduce the so called fermionic field basis. We also extend the analysis to include external electromagnetic fields.

Using this setup we study the problem of pair production in an external electric field at finite temperature. It is found that the production of bosons is enhanced at finite temperature while it is suppressed for fermions. We stress the importance of a finite time analysis.

In the thesis we also solve the Schwinger model within the functional representation in terms of fermionic variables. In particular the gauge-invariant ground-state functional is found. Moreover, we derive bosonisation rules in this formalism.

A system which is studied extensively in the thesis is the charged relativistic boson gas in an external magnetic field. We discuss its thermal properties as well as the properties of the ground state (vacuum). It is found that the magnetisation of the vacuum dominates over the thermal magnetisation at magnetic fields strong enough. The question of condensation in a magnetic field is also addressed. It is verified that `true' Bose-Einstein condensation is impossible in a magnetic field, no matter how weak. However, since there are no discontinuities in the real world, it is shown that the question is somewhat academical.

Finally, we review and study compact charged boson stars. It is shown that the vacuum in the presence of a very compact star is unstable and particles are produced. Numerical evidence for a complete screening of the star by the produced particles is found.

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