This book introduces advanced graduate students and researchers to causal set theory, offering a comprehensive discussion of its core tools. It begins with a broad, largely non-technical overview of causal set theory, situating it within the broader context of the quantum gravity problem. Discreteness and causality serve as the cornerstones of this approach, as articulated by Bombelli, Lee, Meyer, and Sorkin. The technical introduction to causal set theory starts with results on the order-theoretic foundations of Lorentzian geometry, providing a strong theoretical basis. Subsequent chapters address kinematics, including geometrical reconstruction from the discrete substructure, quantum field theory on causal sets, non-perturbative formulations, and results in the quantum dynamics of causal sets. The book concludes with a brief discussion of causal set phenomenology and some open questions.

Written with a clear and pedagogical approach, this book highlights the mathematical challenges inherent in causal set theory. Readers are expected to have prior knowledge of general relativity and quantum field theory. To support understanding, exercises are included throughout the text, enabling readers to test their knowledge.

Provides an in-depth overview of the causal set approach to quantum gravity Highlights key results and open questions in causal set theory Features a pedagogical and self-contained approach, suitable for both beginners and advanced readers

Autorentext

Sumati Surya is a Senior Professor of Physics at the Raman Research Institute in Bengaluru, India, where she has been since 2003. She earned her Ph.D. at Syracuse University, USA, and subsequently held postdoctoral positions in India and Canada. Her research spans mathematical relativity and various aspects of quantum gravity, with a focus on the causal set approach. She has held visiting positions at McGill University, Canada, and the Perimeter Institute, Canada (where she was an Emmy Noether Visiting Fellow), and is currently an adjunct professor at the Dublin Institute for Advanced Studies, Ireland.

Inhalt

Introduction.- Causality in Lorentzian Geometry.- The Causal Set Approach.- Geometry from Order: The Continuum Approximation.- Quantum Dynamics.- Summary of Open Questions and Mathematical Challenges.