Resumen de Quantum states in cosmological spacetimes and entanglement in quantum field theory
Sergi Nadal Gisbert
The theory of quantized fields (QFT) in curved spacetime presents two fundamental challenges. Firstly, there`s the task of explicitly calculating vacuum expectation values of field products such as the stress-energy tensor. This necessitates new regularization and renormalization techniques to address ultraviolet divergences arising from spacetime curvature while maintaining general covariance. Secondly, there`s the issue of selecting a preferred vacuum state. Typically, this is straightforward only for stationary spacetimes or adiabatic regions in expanding universes, where a natural choice of vacuum can be made. However, any physically acceptable quantum state should also satisfy the Hadamard condition, which specifies the singularity structure of the two-point function. The first goal of this thesis is to give new insights into these aspects in a cosmological context. Specifically, the first part of the thesis explores the construction of a pragmatic renormalization method in cosmological spacetimes and the construction of Hadamard vacuum states for homogeneous time-dependent spacetimes, together with its main consequences in a relevant early Universe cosmological scenario.
On the other hand, the incorporation of concepts from quantum information into QFT enables the investigation of fundamental questions regarding locality and information transmission in quantum fields across diverse spacetimes. In particular, the study of entanglement in QFT plays a pivotal role in discerning purely quantum processes and has broad implications ranging from quantum information processing to fundamental physics. The vacuum state of a QFT is a rich state regarding its entanglement structure as revealed by the Reeh-Schlieder theorem. This is usually supported by calculations of entanglement entropy between a region and its complementary one. The results discussed so far pertain to subsystems with infinitely many degrees of freedom, encompassing all field modes within a region. While crucial for grasping quantum field theory conceptually and mathematically, it`s also important to consider finite-dimensional subsystems, as experimentalists only have access to a finite set of degrees of freedom. The second goal of this thesis is to provide an operational approach to study entanglement between a finite set of field modes supported at different regions of space. In addition, we apply these techniques to explore the entanglement structure of the quantum field that underlies in the protocol of Entanglement Harvesting.
