  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.
