Reflection positive one-parameter groups and dilations
| Autor: | Neeb, Karl-Hermann, Olafsson, Gestur |
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| Rok vydání: | 2013 |
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| Druh dokumentu: | Working Paper |
| Popis: | The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the Poincare group from a non-relativistic field theory as a representation of the euclidean motion group. This is the second article in a series on the mathematical foundations of reflection positivity. We develop the theory of reflection positive one-parameter groups and the dual theory of dilations of contractive hermitian semigroups. In particular, we connect reflection positivity with the outgoing realization of unitary one-parameter groups by Lax and Phillips. We further show that our results provide effective tools to construct reflection positive representations of general symmetric Lie groups, including the ax+b-group, the Heisenberg group, the euclidean motion group and the euclidean conformal group. Comment: Final version. To appear in Complex Analysis and Operator Theory |
| Databáze: | arXiv |
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