Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of creation and annihilation operators. The physical motivation for these axioms remains poorly understood, leading to various generalizations by modifying the mathematical formalism in somewhat arbitrary ways. In this work, we take an opposing route and classify quantum particle statistics based on operationally well-motivated assumptions. Specifically, we consider that a) the standard (complex) unitary dynamics defines the set of single-particle transformations, and b) phase transformations act locally in the space of multi-particle systems. We develop a complete characterization, which includes bosons and fermions as basic statistics with minimal symmetry. Interestingly, we have discovered whole families of novel statistics (dubbed transtatistics) accompanied by hidden symmetries, generic degeneracy of ground states, and spontaneous symmetry breaking – effects that are (typically) absent in ordinary statistics.

中文翻译：

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量子粒子统计的重建：玻色子、费米子和跨统计学


相同的量子粒子仅表现出两种类型的统计数据：玻色子和费米子。理论上，这种限制通常是通过对创建和湮灭算子的代数施加的对称化假设或（反）交换约束来建立的。这些公理的物理动机仍然知之甚少，通过以某种任意的方式修改数学形式主义，导致了各种概括。在这项工作中，我们采取了相反的路线，并根据可操作性良好的假设对量子粒子统计数据进行分类。具体来说，我们认为a）标准（复杂）单一动力学定义了单粒子变换集，b）相变在多粒子系统的空间中局部作用。我们开发了完整的表征，其中包括玻色子和费米子作为具有最小对称性的基本统计量。有趣的是，我们发现了一系列新颖的统计（称为反统计），伴随着隐藏的对称性、基态的一般简并性和自发的对称性破缺——普通统计中（通常）不存在的效应。