Abstract
AbstractWe present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in $$(1+1)$$
(
1
+
1
)
- and $$(3+1)$$
(
3
+
1
)
-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
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