标题： SNEG - 用于对第二量子化算子表达式进行符号计算的Mathematica软件包 显示英文标题

标题： SNEG - Mathematica package for symbolic calculations with second-quantization-operator expressions

摘要： 在涉及相互作用费米子或玻色子的多粒子问题中，表达哈密顿量、可观测量和基态的最自然语言是第二量子化算符的语言。 因此，编写允许用户直接以算符字符串形式定义问题和感兴趣量的数值计算机代码是有优势的，而不是使用某种低级编程语言。 在这里，我描述了一个 Mathematica 包，它提供了一个灵活的框架，用于在几种不同的算符表达式表示之间进行所需的转换：使用纯 ASCII 字符串的浓缩符号、传统的符号（“美观打印”）、使用嵌套列表的内部 Mathematica 表示（用于自动符号操作），以及各种高级的（“宏”）表达式。 该包由一组定义算符代数的转换规则和一个全面的实用函数库组成。 虽然重点放在固体物理和原子物理的问题上，但该包可以轻松适应任何涉及非对易算符的问题。 它可以用于教育和演示目的，也可以用于中等规模问题的直接计算。 显示英文摘要

摘要： In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears advantageous to write numerical computer codes which allow the user to define the problem and the quantities of interest directly in terms of operator strings, rather than in some low-level programming language. Here I describe a Mathematica package which provides a flexible framework for performing the required translations between several different representations of operator expressions: condensed notation using pure ASCII character strings, traditional notation ("pretty printing"), internal Mathematica representation using nested lists (used for automatic symbolic manipulations), and various higher-level ("macro") expressions. The package consists of a collection of transformation rules that define the algebra of operators and a comprehensive library of utility functions. While the emphasis is given on the problems from solid-state and atomic physics, the package can be easily adapted to any given problem involving non-commuting operators. It can be used for educational and demonstration purposes, but also for direct calculations of problems of moderate size.