Some Aspects of Quantum Field Theory in NonMinkowskian SpaceTimes
Abstract
This thesis is concerned with several aspects of quantum field theory in spacetimes which are different from Minkowski spacetime. The difference may be due either to the presence of a nonzero curvature, or else be a consequence of the topology of the manifold. An example of quantum field theory in a space time which is flat, but with a topology which is distinct from that of Minkowski spacetime is the Casimir effect. A short review of some of the popular derivations are presented along with comments. The analogy with field theory at a finite temperature is discussed. We also consider why it is sometimes possible to obtain results which are finite by adopting a regularization technique only without the necessity of performing renormalization, and discuss some limitations of this. Renormalization of interacting scalar field theories in a flat spacetime with a nonMinkowskian topology is considered. The SchwingerDyson equations for a general scalar field theory with a quartic interaction are derived using functional techniques. An introduction to twisted fields is presented. The renormalization of interacting twisted and untwisted scalar fields to second order in perturbation theory in a flat spacetime with the topology S('1) x R('3) is discussed. It is seen that the presence of a nontrivial topology can lead to additional nonlocal divergent terms, beyond those divergences which are present in Minkowski spacetime; however, when all graphs of the same order are combined, all such nonlocal divergences cancel among each other, and the theory may be renormalized with the same choice of counterterms as in Minkowski space time. A further feature which is discussed is that the existence of a nontrivial topology can cause the propagators to develop poles corresponding to the generation of a topological mass. The functional approach to the effective potential is reviewed, and it is shown how zetafunction regularization fits naturally into this scheme. This formalism is applied to calculate the effective potential for some scalar field theories in nonMinkowskian spacetimes. Topological mass generation is discussed, and it is also shown how radiative corrections can lead to spontaneous symmetry breaking in some cases. One and twoloop contributions to the vacuum energy density are obtained for both massless and massive fields. In the massive case the role of renormalization in removing nonlocal divergences is discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT........95T
 Keywords:

 Physics: Elementary Particles and High Energy