Timeless Quantum Mechanics and the Early Universe

The book is based on the author's PhD thesis, which deals with the concept of time in quantum gravity and its relevance for the physics of the early Universe. It presents a consistent and complete new relational formulation of quantum gravity (more specifically, of quantum mechanics models with diffeomorphism invariance), which is applied to potentially observable cosmological effects. The work provides answers to the following questions: How can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? The answers can provide a further part of the route to constructing a fundamental theory of quantum gravity. The book is well-suited to graduate students as well as professional researchers in the fields of general relativity and gravitation, cosmology, and quantum foundations.

Autorentext

Leonardo Chataignier completed his PhD degree in Theoretical Physics at the University of Cologne (Germany) with the highest distinction (summa cum laude) in 2021. His research focuses on quantum gravity and quantum cosmology, and more specifically on the investigation of the consequences of diffeomorphism invariance to the formalism of quantum mechanics. His PhD thesis presents a new method of relating quantum states to probabilities without an external or preferred time parameter, and of describing the quantum dynamics in a diffeomorphism-invariant way. This method may facilitate the construction and conceptual understanding of a fundamental theory of quantum gravity. Before his PhD work, Chataignier completed his Master's degree (MSc) in Theoretical Physics at Utrecht University (The Netherlands) with the highest distinction (cum laude) in 2017, and his Bachelor's degree (BSc) in Physics with a Certificate of Additional Studies in Mathematics at the Pontifical Catholic University of Rio de Janeiro (Brazil) in 2014, having received a number of "Prizes for Academic Merit'', a "Prize for Outstanding Undergraduate Research'', as well as a "Physics Challenge Scholarship'', which covered the tuition fees for the duration of his Bachelor's studies (2011-2014).

Inhalt

Introduction.- Classical Diffeomorphism Invariance on the Worldline.- Quantum Diffeomorphism Invariance on the Worldline. The Relativistic Particle as an Archetypical Example.- Homogeneous Classical and Quantum Cosmology.- Weak-Coupling Expansion-. Quantum-Gravitational Effects in the Early Universe.- Conclusions and Outlook.- Appendix A Review of Gauge Systems and Constrained Dynamics.- Appendix B. The Traditional Born-Oppenheimer Approach to the Problem of Time.