Quantum Vacuum Dynamics: Exploring The Impacts of Acceleration, Rotation and Boundaries in Interacting Quantum Field Theory

Quantum fluctuations and zero-point energy are cornerstones of quantum field theory, representing the ever-present quantum corrections to classical fields. These phenomena, which embody the intrinsic properties of the quantum vacuum, play a profound role in shaping the physical behaviour of a given system. This thesis investigates how these quantum contributions behave under three specific influences: acceleration, rotation, and boundaries, particularly for self-interacting fields. Motivated by unresolved issues or discrepancies in the literature, this work seeks to shed light on the complex nuances of this subject. Specifically, the first problem addressed focuses on the phenomenon of symmetry breaking and the possible associated restoration induced by acceleration via the Unruh effect. Fundamental physical principles are challenged in this matter. For a broken symmetry to be restored by a change in the reference frame, it implies that the concept of scalar quantities breaks down at the quantum level. Conversely, if symmetry breaking persists, the interpretation of the Unruh effect as a genuine thermodynamic phenomenon comes into question. Given the lack of consensus on symmetry restoration, this work examines the various methods for calculating quantum corrections and identifies how the differing renormalization prescriptions lead to the contrasting outcomes across the existing literature. The second investigated issue examines the quantum vacuum energy in non-relativistic (Schrödinger) quantum field theories. While these theories are typically not influenced by zero-point energy, it is shown that such contributions cannot be neglected when, in addition to Dirichlet boundary conditions, rotations and interactions are considered. In this framework, the calculation of the unperturbed spectrum reveals a non-vanishing quantum vacuum energy, along with a Casimir-like force that includes both a repulsive contribution from rotation and an attractive contribution from interactions. These results are further corroborated by examining the corresponding relativistic theory, ensuring consistency with the non-relativistic limit. The novel contributions to the interacting quantum vacuum, combined with the potential for experimental verification through systems such as Bose-Einstein condensates, provide a compelling motivation for further exploration of these phenomena.