Particles in Quantum Field Theory and Non-inertial Reference Frames

Abstract

In this thesis I discuss various topics relating to the definition of particles and vacuum states in quantum field theory in general, and apply it to non-inertial reference frames in Minkowski spacetime. The particle concept in quantum field theory is shown to be rather ambiguous and subjective.

I discuss generally what particles are and how they should be defined in quantum field theories. I then discuss what ambiguities are inherent in such a definition and in particular what ambiguities there are for observers in different stationary non-inertial reference frames in Minkowski spacetime. I use this to gain a broader perspective on the Unruh effect, the effect by which an accelerated observer will view the vacuum state of an inertial reference frame as being filled by a thermal ensemble of particles. I conclude that the effect actually depends on how the solutions of the field equation are joined across the event horizon that is present in hyperbolicly accelerated reference frames, and that the effect is really more subjective than is commonly assumed in the literature. Finally, I investigate the behaviour of a model particle detector. I conclude that it does not necessarily reflect the spectrum of particles that is present in the reference frame of the detector, because the excitation spectrum of the detector may be distorted by particle states with negative energy, which are present in many non-inertial reference frames. The results of detection experiments will therefore not generally agree with the usual definition of particles in quantum field theory.

Along the way I provide explicit calculations of all possible Killing vector fields and stationary trajectories in Minkowski spacetime, discussions of what the corresponding reference frames look like, as well as solutions of the Klein-Gordon equation in coordinates appropriate to the different reference frames.