量子F_un:伽罗瓦场量子力学、射影几何和单元场的q=1极限
Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element
摘要:
我们认为,构造在伽罗瓦场F_q=GF(q)上的向量空间上的伽罗瓦场量子力学的q=1极限对应于它的“经典极限”,在经典极限中态的叠加是不允许的。该极限保留了状态空间的射影几何性质,并且可以理解为在“具有一个元素的域”F_1上的“向量”空间的适当定义的类似物上构造。
英文摘要:
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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