从$SO(3)_p$的不可约表示求$p$ -adic量子比特
An approach to $p$-adic qubits from irreducible representations of $SO(3)_p$
摘要：
在Volovich等人提出并发展的$p$-adic量子力学的基础上，引入了$p$-adic量子比特（$p$ -qubit）的概念.在这种方法中，物理发生在三维$p$ -adic空间而不是欧几里得空间中。基于我们以前的工作描述的$p$ -adic特殊正交群，我们概述了一个程序来分类其连续酉射影表示，这可以被解释为一个理论的$p$ -adic角动量。$p$ -adic量子比特产生于最小非平凡维数2的不可约表示，我们构造了所有素数$p$的例子。
英文摘要：
We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space. Based on our prior work describing the $p$-adic special orthogonal group, we outline a programme to classify its continuous unitary projective representations, which can be interpreted as a theory of $p$-adic angular momentum. The $p$-adic quantum bit arises from the irreducible representations of minimal nontrivial dimension two, of which we construct examples for all primes $p$.
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