Quantum field theory and acausal spacetimes

This thesis is concerned with various problems that arise when one attempts to quantise fields on spacetimes which contain regions of closed time-like curves (CTCs). Chapter 1 presents a review of some of the major classical and quantum difficulties encountered by various authors investigating acausal spacetimes until 1993. In chapter 2, a number of more recent proposals that have been put forward in an attempt to construct a consistent dynamics are considered. Particular consideration is given to the density matrix proposal for Deutsch and Politzer, which is ultimately shown to give a nonlinear evolution through the acausal region. This work has been published in Phys. Rev. D 52, 5676 (1995). The chapter concludes with a discussion of the Euclidean approach, which is adopted by this author for much of the remainder of the thesis. It is argued that the inevitable loss of quantum coherence is physically preferable to the nonlinear evolution encountered in the other proposals. Chapter 3 is concerned with the effective action for matter fields defined on acausal spacetimes, in which an expression is derived for the 1 loop effective action for fields for arbitrary mass and spin on Euclidean spaces which have acausal analytic continuations. I will show that in general, after one has analytically continued back to the acausal section, the effective action diverges to minus affinity at each of the nth polarised hypersurfaces of the spacetime with a structure governed by a de Witt-Schwinger type expansion. In particular, I will show that even if →T_μνπ remains finite at the Cauchy horizon, the effective action will still diverge there. This work has been published in Classical and Quantum Gravity 14, 3031 (1997). In chapter 4 I attempt to give a sensible interpretation to Euclidean path integrals in the presence of causality violations, which was work carried out in collaboration with S.W. Hawking. If the action always diverges to minus infinity, then at first sight it seems as if any Euclidean path integrals will be completely ill defined. However, I will argue that if one focuses on the density of states, one can obtain physically reasonable results. Ultimately, I will derive an expression for the effective action of a boosted scalar field configuration in the product of three dimensional de Sitter space and S¹, and I consider the number of states with a fixed linear momentum around the S¹ as the particles are given more and more boost momentum. I will show that at the critical point when the spacetime is about to develop closed timelike curves, the number of states tends to zero. This suggest that quantum mechanics naturally enforces the Chronology Protection Conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space. This work has been accepted for publication in Phys. Rev. D. Finally, in chapter 5 I consider what happens when one includes the effects of back reaction in a spacetime containing CTCs. Misner space is considered as an axisymmetric Bianchi I universe and it is assumed that near the horizon, the periodic identification in the x direction provides the dominant contribution to the energy-momentum tensor. I will show that, as the horizon is approached, any small perturbation grows until a singularity forms in a finite proper time, which therefore lends further support to the Chronology Protection Conjecture. This work has been submitted for publication to Classical and Quantum Gravity and is the subject of DAMTP preprint R/98/01.