Reflection Positivity A Representation Theoretic Perspective /

• Κύριοι συγγραφείς: Neeb, Karl-Hermann (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Ólafsson, Gestur (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: SpringerBriefs in Mathematical Physics, 32
• Θέματα: Topological groups.; Lie groups.; Quantum field theory.; String theory.; Mathematical physics.; Harmonic analysis.; Probabilities.; Topological Groups, Lie Groups.; Quantum Field Theories, String Theory.; Mathematical Physics.; Abstract Harmonic Analysis.; Probability Theory and Stochastic Processes.

Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the representation theoretic aspects of Refection Positivity and...

Πίνακας περιεχομένων:

• Preface
• Introduction
• Reflection positive Hilbert spaces
• Reflection positive Hilbert spaces
• Reflection positive subspaces as graphs
• The Markov condition
• Reflection positive kernels and distributions
• Reflection positivity in Riemannian geometry
• Selfadjoint extensions and reflection positivity
• Reflection positive representations
• The OS transform of linear operators
• Symmetric Lie groups and semigroups
• Reflection positive representations
• Reflection positive functions
• Reflection positivity on the real line
• Reflection positive functions on intervals
• Reflection positive one-parameter groups
• Reflection positive operator-valued functions
• A connection to Lax-Phillips scattering theory
• Reflection positivity on the circle
• Positive definite functions satisfying KMS conditions
• Reflection positive functions and KMS conditions
• Realization by resolvents of the Laplacian
• Integration of Lie algebra representations
• A geometric version of Fr¨ohlich's Selfadjointness Theorem
• Integrability for reproducing kernel spaces
• Representations on spaces of distributions
• Reflection positive distributions and representations
• Reflection positive distribution vectors
• Distribution vectors
• Reflection positive distribution vectors
• Spherical representation of the Lorentz group
• Generalized free fields
• Lorentz invariant measures on the light cone and their relatives
• From the Poincar´e group to the euclidean group
• The conformally invariant case
• Reflection positivity and stochastic processes
• Reflection positive group actions on measure spaces
• Stochastic processes indexed by Lie groups
• Associated positive semigroup structures and reconstruction
• A Background material
• A.1 Positive definite kernels
• A.2 Integral representations
• Index.