标题： 第二量子化中的玻色子-费米子代数映射 显示英文标题

标题： Boson-fermion algebraic mapping in second quantization

摘要： 我们提出一种代数方法，以推导玻色算符的产生和湮灭算符代数映射到费米算符代数，反之亦然的基础结构，并引入玻色和费米生成元之间的适当识别。由此获得的代数结构对应于一种变形的格拉斯曼代数，涉及反对易的格拉斯曼型变量。随后讨论了后者在我们程序中实现规范不变性的角色，以及该映射在玻色和费米谐振子哈密顿量情况下的应用。 显示英文摘要

摘要： We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann algebra, involving anticommuting Grassmann-type variables. The role played by the latter in the implementation of gauge invariance in second quantization within our procedure is then discussed, together with the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians.