Symmetrization of the product of Hermitian operators


The symmetrization process of the product of Hermitian operators is computerized. Indeed, we write a rather general code under Mathematica and Python which can be used for symmetrizing any kind of product of Hermitian operators including a linear combination of such operators with respect to some weight functions.

Program summary

Program Title: SymPHO

CPC Library link to program files:

Licensing provisions: GPLv3

Programming language: Mathematica, Python

Nature of problem: The symmetrization of products of Hermitian operators is a well-known problem. Such a symmetrization process would be very time consuming when considering an operator made of the product of more than two terms. According to two different scenarios, the calculation of fully symmetric forms of products of Hermitian operators is computerized.

Solution method: SymPHO outputs the fully symmetric forms of a list of given operators in index form by calculating the permutations of each operator. After determining the free indices and the indices to summed over, it moves the derivative terms to the far right by applying a test function. In the first scenario in which each operator is symmetrized independently, it gives a symmetric form that is the sum of the results coming from all permutations normalized by the number of permutations. For the second scenario in which one needs to symmetrize each term of the linear combination of a set of operators, it symmetrizes each permutation with its Hermitian couple and outputs the result with the minimum length.

In Computer Physics Communications