The de Sitter (dS) Group and Its Representations
An Introduction to Elementary Systems and Modeling the Dark Energy Universe
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Beschreibung
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.
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
Autor*in
Mohammad Enayati
Themen in »The de Sitter (dS) Group and Its Representations«
de Sitter Relativity de Sitter Group Representations Group Contraction Quantum Field Theory Curved Spacetimes Cosmological Constant Dark Energy Co-adjoint Orbit Phase Space Realization de Sitter Plane Waves Wightman-Gärding Axioms
Stimmen zu »The de Sitter (dS) Group and Its Representations«
“The book is accessible for both experts in cosmology and beginners.” (Alex B. Gaina, zbMATH 1552.83169, 2025)
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