The de Sitter (dS) Group and Its Representations: Synthesis Lectures on Mathematics & Statistics
Autor Mohammad Enayati, Jean-Pierre Gazeau, Hamed Pejhan, Anzhong Wangen Limba Engleză Paperback – mai 2025
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| Paperback (2) | 307.93 lei 3-5 săpt. | |
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| Hardback (2) | 323.22 lei 38-44 zile | |
| Springer International Publishing – dec 2022 | 323.22 lei 38-44 zile | |
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Specificații
ISBN-13: 9783031565540
ISBN-10: 3031565541
Pagini: 260
Dimensiuni: 168 x 240 x 15 mm
Greutate: 0.44 kg
Ediția:Second Edition 2024
Editura: Springer
Seria Synthesis Lectures on Mathematics & Statistics
ISBN-10: 3031565541
Pagini: 260
Dimensiuni: 168 x 240 x 15 mm
Greutate: 0.44 kg
Ediția:Second Edition 2024
Editura: Springer
Seria Synthesis Lectures on Mathematics & Statistics
Cuprins
Introduction.- 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.
Notă biografică
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.
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.
Textul de pe ultima copertă
This book reviews the construction of elementary systems living in de Sitter (dS) spacetime, in both the classical and quantum senses. Field theories on dS spacetime are among the most studied mathematical models of the Universe, whether for its earlier period (inflationary phase) or for its current phase of expansion acceleration (dark energy or cosmological constant). Classical elementary systems are Hamiltonian phase spaces, which are associated with co-adjoint orbits of the relativity group. On the other hand, quantum elementary systems are associated with (projective) unitary irreducible representations of the (possibly extended) relativity group (or one of its covering). This study emphasizes the conceptual issues arising in the formulation of such systems and discusses known results in a mathematically rigorous way. Particular attention is paid to: “smooth” transition from classical to quantum theory; physical content under vanishing curvature, from the point of view of a local(“tangent”) Minkowskian observer; and thermal interpretation (on the quantum level), in the sense of the Gibbons-Hawking temperature. Such a mathematical construction is of paramount importance to the understanding of the early Universe (due to the critical role that the dS metric plays in the inflationary cosmological scenarii) as well as to the construction of possible models for late-time cosmology (since a small positive cosmological constant or dark energy seems to be required by recent data). In this sense, this book uniquely blends mathematical physics (spacetime symmetry on classical and quantum levels) and theoretical physics (quantization, quantum field theory, and cosmology). Moreover, the level of exposition varies in different parts of the book so that both experts and beginners alike can utilize the book.
In addition, this book:
- Presents consistent formulations of dS elementary systems on three levels; classical mechanics,quantum mechanics, and the quantum field theory
- Blends mathematical physics (spacetime symmetry on classical and quantum levels) and theoretical physics (quantization, quantum field theory, and cosmology) to uniquely introduce the mathematical structure of dS relativity
- Discusses conceptual considerations/worries that arise in the formulation of elementary systems
Caracteristici
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