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 )