This Second Edition is a comprehensive update, integrating the latest research and theoretical advancements in the field of de Sitter (dS) group representations. Building on the success of the first edition, the book offers a more in-depth analysis of mathematical aspects, conceptual foundations, and practical implications related to the dS group, including its Lie manifold, Lie algebra, and co-adjoint orbits, viewing the latter as potential classical elementary systems within the context of dS spacetime. Additionally, the examination of unitary irreducible representations (UIRs) sheds light on the potential existence of quantum elementary systems within the dS spacetime framework. The authors emphasize consistency with Wigner's approach to elementary systems, incorporate Wigner's principles and exploring projective UIRs of the dS group, and provide a deeper insight into the nature of dS elementary systems. Particular attention is paid to: the smooth transition from classical to quantum theory, the physical content under vanishing curvature, and the thermal interpretation from a quantum perspective. The book also focuses on the physical interpretation of elementary systems in curved spacetimes, recognizing the limitations of traditional concepts derived from flat Minkowski spacetime and the Poincaré group.

Delves into the mathematical intricacies of the de Sitter (dS) group and its unitary irreducible representations (UIRs) Explores the meticulous construction of dS elementary systems, aligned with the Wigner framework and UIRs Offers a unique grasp of inflationary and late-time cosmology in classical and quantum realms

Autorentext

Mohammad Enayati, Ph.D., is a Resident Researcher at Razi University where he received his Ph.D. in theoretical physics in 2017. He has also been a visiting researcher at Azad University and Zhejiang University of Technology. His research interests include group-theoretical methods in physics, with an emphasis on de Sitter (spacetime) symmetry considerations on both classical and quantum levels.

Jean-Pierre Gazeau, Ph.D., is an Emeritus Professor at the University Paris Cité. He was chairman of the Standing Committee of the International Colloquium on Group Theoretical Methods in Physics from 2006 to 2014. He obtained his academic degrees from Sorbonne University and Pierre-and-Marie Curie University. He has authored more than 252 scientific publications, including three books, in theoretical and mathematical physics, mostly devoted to group theoretical methods in physics, coherent states, quantization methods, number theory for aperiodic systems, and foundations of quantum physics.

Hamed Pejhan, Ph.D., is a Senior Postdoctoral Researcher at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Dr. Pejhan previously served as a Postdoctoral Fellow at Zhejiang University of Technology. He has authored more than 20 scientific publications in theoretical and mathematical physics, primarily focusing on the application of group theoretical methods in physics. His research pays particular attention to developing a consistent formulation of quantum elementary systems in (anti-) de Sitter spacetime.

Anzhong Wang, PhD, is a Professor from Physics Department, Baylor University. His research interests include classical and quantum theories of gravity, their applications to cosmology and black hole physics; gravitational wave astronomy, and the nature and origins of dark matter and dark energy. He has published more than 290 articles and received approximately10,000 citations. He has been among the top 2% cited world scientists over all science fields in recent years.

Inhalt
Introduction.- As a preliminary: 1 + 1-dimensional dS (dS2) geometry and relativity.- 1+3-dimensional dS (dS4) geometry and relativity (classical and quantum mechanics).- 1+3-dimensional dS (dS4) geometry and relativity (QFT).- Notion of mass in (A)dS4 relativity.