99-400 Johanna Gaier, Jakob Yngvason

Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields} (39K, latex2e) Oct 20, 99

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Abstract. The Tomita-Takesaki modular groups and conjugations for the observable algebras of space-like wedges and the vacuum state are computed for translationally covariant, but possibly not Lorentz covariant, generalized free quantum fields in arbitrary space-time dimension $d$. It is shown that for $d\geq 4$ the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers \cite{BDFS}, Lorentz covariance and wedge duality are all equivalent in these models. The same holds for $d= 3$ if there is a mass gap. For massless fields in $d=3$, and for $d=2$ and arbitrary mass, CGMA does not imply Lorentz covariance of the field itself, but only of the maximal local net generated by the field.

Files: 99-400.src( 99-400.keywords , gaier_zeros.tex )