ESI The Erwin Schr odinger
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چکیده
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 elds in arbitrary space-time dimension d. It is shown that for d 4 the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig and Summers BDFS], Lorentz covariance and wedge dual-ity are all equivalent in these models. The same holds for d = 3 if there is a mass gap. For massless elds in d = 3, and for d = 2 and arbitrary mass, CGMA does not imply Lorentz covariance of the eld itself, but only of the maximal local net generated by the eld.
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ESI The Erwin Schr odinger
2 ABSTRACT In this paper we explicitly prove the invariance of the time-dependent string gravity Lagrangian with up to four derivatives under the global O(d; d) symmetry.
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3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...
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