EAN: 9783031160479

SYNTHESIS LECTURES ON MATHEMATICS & STATISTICS ...

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.

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