04510nam a22006135i 4500 978-3-031-56552-6 DE-He213 20251030112019.0 cr nn 008mamaa 240429s2024 sz | s |||| 0|eng d 9783031565526 978-3-031-56552-6 10.1007/978-3-031-56552-6 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Enayati, Mohammad. author. aut http://id.loc.gov/vocabulary/relators/aut 76014 The de Sitter (dS) Group and Its Representations [electronic resource] : An Introduction to Elementary Systems and Modeling the Dark Energy Universe / by Mohammad Enayati, Jean-Pierre Gazeau, Hamed Pejhan, Anzhong Wang. 2nd ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XV, 241 p. 16 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Mathematics & Statistics, 1938-1751 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. 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. In addition, this book: 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. Mathematical physics. Astrophysics. 68037 Cosmology. 76015 Elementary particles (Physics). 68885 Quantum field theory. 68886 Mathematical Physics. Astrophysics. 68037 Cosmology. 76015 Theoretical, Mathematical and Computational Physics. 65563 Elementary Particles, Quantum Field Theory. 68887 Mathematical Methods in Physics. 70877 Gazeau, Jean-Pierre. author. aut http://id.loc.gov/vocabulary/relators/aut 76016 Pejhan, Hamed. author. aut http://id.loc.gov/vocabulary/relators/aut 76017 Wang, Anzhong. author. aut http://id.loc.gov/vocabulary/relators/aut 76018 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031565519 Printed edition: 9783031565533 Printed edition: 9783031565540 Synthesis Lectures on Mathematics & Statistics, 1938-1751 https://doi.org/10.1007/978-3-031-56552-6 ZDB-2-SXSC 59500 59500