Bohrification of local nets of observables
Bohrification of local nets of observables
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发表时间：
2011-09
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通讯作者：
J. Nuiten
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作者：
J. Nuiten
Spitters et.的最新结果。建议量子相空间可以有效地被视为通过称为Bohrification的过程的环形拓扑。他们表明，量子运动学可以被解释为经典运动学，内部的环形拓扑结构。我们将这些思想从量子力学扩展到代数量子场论：从一个可观测的网络中，我们构造了一个量子相空间的预层。然后，我们可以自然地表示因果局部性的网络作为一个下降的条件，相应的预层的环toposes：我们表明，净的可观的是本地的，正是当预层的环toposes满足下降的局部几何态射。
Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics can then be interpreted as classical kinematics, internal to this ringed topos. We extend these ideas from quantum mechanics to algebraic quantum field theory: from a net of observables we construct a presheaf of quantum phase spaces. We can then naturally express the causal locality of the net as a descent condition on the corresponding presheaf of ringed toposes: we show that the net of observables is local, precisely when the presheaf of ringed toposes satisfies descent by a local geometric morphism.