Understand
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.