Basis of symmetric polynomials for many-boson light-front wave functions

TL;DR

This paper introduces an algorithm to construct symmetric, orthonormal multivariate polynomials on a constrained hypercube, providing a basis for expanding many-boson light-front wave functions in quantum field theory.

Contribution

It generalizes previous work to arbitrary numbers of bosons, enabling systematic expansion of bosonic wave functions with momentum conservation constraints.

Findings

Constructed explicit polynomial basis for any number of bosons.

Demonstrated application in two-dimensional $$ theory.

Facilitated more efficient wave function expansions.

Abstract

We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the coordinates is one. These polynomials form a basis for the expansion of bosonic light-front momentum-space wave functions, as functions of longitudinal momentum, where momentum conservation guarantees that the fractions are on the interval $[0,1]$ and sum to one. This generalizes earlier work on three-boson wave functions to wave functions for arbitrarily many identical bosons. A simple application in two-dimensional $\phi^4$ theory illustrates the use of these polynomials.