标题： 具有最大总占据性质的广义玻色子和费米子算符 显示英文标题

标题： Generalized boson and fermion operators with a maximal total occupation property

摘要： 我们提出了一种标准（反）对易关系的新推广，这些关系适用于玻色子和费米子的产生与湮灭算符。 这些关系保留了玻色子和费米子通常的对称性质。 仅涉及一个产生算符和一个湮灭算符的标准（反）对易关系通过引入含正整数参数$p$的分数系数而发生变形。 Fock 空间由经典的定义确定。 新的关系被选择为使得系统中的总占据数达到最大值$p$。 通过对 Fock 空间中产生和湮灭算符的作用，确定了一个群论框架，并由此建立了与已知粒子统计学的对应关系。 显示英文摘要

摘要： We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter $p$. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value $p$. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.