Title:

Fermions from timedependent boundaries : stressenergy versus clicks of a particle detector

In this thesis, we analyse massless fermion creation by timedependent boundaries in (1+1)dimensional flat spacetimes. We consider two distinct senses in which the boundaries are said to be timedependent. On one hand, we study a boundary which remains at rest with respect to a family of inertial observers but imposes a timedependent boundary condition. On the other hand, we study a boundary that moves along a timelike trajectory while imposing a timeindependent boundary condition, that is the MIT bag boundary condition. In both cases, we calculate the stressenergy tensor of the spinor field describing the fermions, renormalised via the pointsplitting method, and the response of an inertial UnruhDeWitt detector coupled linearly to the scalar density of the field. Throughout our analysis, we compare our results to those readily available in the literature for a massless scalar field in similar settings. In the motionless evolving wall analysis, we first consider a wall that imposes a generic boundary condition parametrised by four arbitrary timedependent functions. Some of the boundary conditions may be interpreted as arising from a combination of idealised scalar and electric potentials. We find that the wall generates an energy burst of finite magnitude when the evolution is smooth. The response of an inertial detector passing through the generated energy burst is also finite. We then analyse an evolving wall that simulates the creation or demolition of a wall that imposes a doublesided MIT bag boundary condition. In the limit of rapid MIT wall creation or demolition, the energy burst displays a delta function squared divergence but, within first order perturbation theory, the detector response diverges only logarithmically in the duration of wall evolution. The results add to the evidence that a localised matter system may not be as sensitive to the divergence in local expectation values of field observables such as the stressenergy tensor. In the moving wall analysis, we first consider a wall that moves along an arbitrary timelike trajectory. We find that the stressenergy tensor of the field is identical to that of a massless scalar field in the moving mirror spacetime. By contrast, we find that the transition rate of an inertial UnruhDeWitt detector coupled linearly to the scalar density of the spinor field is generically different from that of a detector coupled linearly to a scalar field or its derivative. Hence, an observer examining just the stressenergy tensor sees no difference between a fermion and a boson, neither at late times nor early, while an observer equipped with an UnruhDeWitt detector will generically be able to distinguish fermions from bosons. We then analyse a wall trajectory for which a mirror scattering a scalar field following the same trajectory is known to emit thermal radiation in the far future. We find that the late time transition rate of the fermionic detector is proportional to the Helmholtz free energy density of a fermionic thermal bath, hence showing a clear sign of FermiDirac statistics, with no counterpart in the response of a scalar detector.
