• Walter Thirring


The framework for this discussion will be an algebra A of observables with a strongly continuous time-automorphism and a time-invariant state ρ In the GNS representation the invariant state is made into a vector \(\left| \Omega \right\rangle \), and the timeautomorphism is represented as a unitary group of operators \(U = \left\{ {\exp (iHt)} \right\},U\left| \Omega \right\rangle = \left| \Omega \right\rangle \). The time-evolution then extends to the weak closure A″. If the representation is reducible, then it may occur that UA″, even if \(U_t^{ - 1}A{U_t} \subset A.\) The von Neumann algebra
$$ R \equiv {\left\{ {A \cup U} \right\}^{\prime \prime }},R' = A' \cap U', $$
generated by A and U is known as the covariance algebra and will figure prominently in what follows.


Relative Entropy Invariant State Infinite System Free Fermion Invariant Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Walter Thirring
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of ViennaViennaAustria

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