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SpringerBriefs in Mathematical Physics

Reflection Positivity

A Representation Theoretic Perspective

Authors: Neeb, Karl-Hermann, Olafsson, Gestur

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About this book

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 discusses its connections to those different fields on a level suitable for doctoral students and researchers in related fields.

It starts with a general introduction to the ideas and methods involving refection positive Hilbert spaces and the Osterwalder--Schrader transform. It then turns to Reflection Positivity in Lie group representations. Already the case of one-dimensional groups is extremely rich.

For the real line it connects naturally with Lax--Phillips scattering theory and for the circle group it provides a new perspective on the Kubo--Martin--Schwinger (KMS) condition for states of operator algebras. 

For Lie groups Reflection Positivity connects unitary representations of a symmetric Lie group with unitary representations of its Cartan dual Lie group.

A typical example is the duality between the Euclidean group E(n) and the Poincare group P(n) of special relativity. It discusses in particular the curved context of the duality between spheres and hyperbolic spaces. Further it presents some new integration techniques for representations of Lie algebras by unbounded operators which are needed for the passage to the dual group. Positive definite functions, kernels and distributions and used throughout as a central tool.


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-94755-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-94754-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Reflection Positivity
Book Subtitle
A Representation Theoretic Perspective
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
32
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-94755-6
DOI
10.1007/978-3-319-94755-6
Softcover ISBN
978-3-319-94754-9
Series ISSN
2197-1757
Edition Number
1
Number of Pages
VIII, 139
Topics