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arXiv · 1312.4191

Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element

Lay Nam Chang·Zachary Lewis·Djordje Minic·Tatsu Takeuchi
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Abstract

We argue that the q=1 limit of Galois Field Quantum Mechanics, which was constructed on a vector space over the Galois Field F_q=GF(q), corresponds to its `classical limit,' where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a `vector' space over the `field with one element' F_1.

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Lay Nam Chang, Zachary Lewis, Djordje Minic, Tatsu Takeuchi. 2013-12-15. Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element. https://doi.org/10.1088/1751-8113/47/40/405304

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