 94153 Borchers H.J.
 Theory of Local Observables and KMSCondition
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Jun 1, 94

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Abstract. We will look at C$^*$dynamical systems with the translations of $\BR^d$
as dynamical group and will define KMSfunctionals for $\beta$ taking
values in $\BC^d$. The properties of such functionals will be investigated.
In particular if a KMSfunctional exists for a complex $\beta$ then
it will be shown that there exists a KMSstate for the real part of $\beta$.
If the system is a theory of local observables then it will be shown that
locality condition implies that there do not exist $\beta$KMSfunctionals
such that $\beta$ is spacelike or has a spacelike real part.
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