Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum observable corresponds to a unitary representation of an abelian Lie group, the irreducible subrepresentations of which correspond to the observable's outcomes. It is shown that this identification agrees with the conventional identification as self-adjoint operators. The upshot of this formalism is that one may 'second quantize' the representation to which an observable corresponds, thus obtaining the corresponding Fock space representation. This Fock space representation is then also identifiable as an observable in the same sense, the outcomes of which are naturally interpretable as ensembles of outcomes of the corresponding non-second quantized observable. The frequency interpretation of probability is adopted, i.e. probability as the average occurrence, from which Born's rule is deduced by enforcing the notion of 'average' to such that are invariant under the second quantized unitary representation which defines the quantum observable to which the initial state is an outcome. The enforcement of this invariance is an application the principle referred to as the 'principle of unitary equivalence'.

中文翻译：

---

从酉等价原理看玻恩法则

复相位因子不仅被视为量子形式主义的冗余，而且被视为幺正变换的残余，在这种变换下，可观测值的概率特性是不变的。假设量子可观测对应于阿贝尔李群的酉表示，其不可约子表示对应于可观测的结果。结果表明，这种识别与作为自伴随算子的常规识别一致。这种形式主义的结果​​是，人们可以“二次量化” observable 对应的表示，从而获得相应的 Fock 空间表示。这个 Fock 空间表示在同样的意义上也可以被识别为一个可观察的，其结果自然可以解释为相应非第二量化可观察结果的集合。采用概率的频率解释，即概率作为平均出现，通过强制“平均”的概念推导出玻恩规则，使得在定义初始状态的量子可观测的第二量化幺正表示下是不变的。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?是一个结果。这种不变性的实施是一项被称为“单一等价原则”的原则的应用。到这样的在第二个量化的幺正表示下是不变的，该表示定义了初始状态是其结果的量子可观察量。这种不变性的实施是一项被称为“单一等价原则”的原则的应用。到这样的在第二个量化的幺正表示下是不变的，该表示定义了初始状态是其结果的量子可观察量。这种不变性的实施是一项被称为“单一等价原则”的原则的应用。