Investigations of the Phase Transition in QED on the Lattice

The aim of this project is the investigation of some aspects concerning the phase transition in compact quantum electrodynamics (CQED). This theory is a formulation of quantum electrodynamics on a discrete lattice in space and time. The artificial introduction of a discrete lattice of finite size clearly influences physical results. At the end of the calculations the continuous limit is performed, this means that all calculated variables are evaluated for diminishing small distances between the lattice points. Up to now, all calculations were done with point like magnetic monopoles, which are placed inside the lattice cubes. The influence of the lattice is felt in the movement of these monopoles. In this project a new theory is applied for the first time which enables to perform calculations for monopoles of arbitrary size. If a monopole extends over several lattice cubes the influence of a single cube on the movement of the extended monopole is much smaller than the influence on point like monopoles which were used in former investigations. In this project the software was developed which enables to perform calculations with point like and extended monopoles. First, it was shown that the former results can be reproduced with the software and point like monopoles. Furthermore, it was shown that the new theory of extended monopoles yields the same physical results as point like monopoles in the limit of vanishing extension. Former calculations have shown that there are two phases in CQED. In one of these, the coulombic phase, the theory appears in complete agreement with experience that means electric charges exist which interact by electric and magnetic fields. The second phase is the confinement phase. In this phase magnetic charges, that means magnetic monopoles, appear which tie up electric fields thus creating the so called confinement. Unlike charges are bound since the potential between them increases linearly with their relative distance. The phase transition in CQED is either a first or second order transition. In the case of first order phase transitions there does not exist a continuous limit, i.e. there is no transition from the formulation on the lattice to the one in continuous space-time. In the case of a second order phase transition a continuous limit exists, which is an important condition for the validity of the theory. Thus, the determination of the order of this phase transition is of crucial importance. Since the 1980s there are investigations to determine the order of the phase transition. Up to now, no unique result has been obtained since there are hints for both, a phase transition of first order and second order. The performed simulations show that the phase transition dependents on the size of the monopoles. Thus, the introduction of a space-time lattice influences the phase transition essentially. Further investigations are done in order to evaluate the order of the phase transition in the above described extended version of CQED under consideration of these new results.