Symmetric multivariate polynomials as a basis for three-boson light-front wave functions

TL;DR

This paper introduces a symmetric polynomial basis for three-boson light-front wave functions, improving numerical calculations by exploiting symmetry and polynomial properties, demonstrated in a phi^4 theory example.

Contribution

The authors develop a symmetric polynomial basis on a triangular domain for three-boson wave functions, enhancing computational efficiency over traditional plane-wave methods.

Findings

Polynomial basis is unique up to fifth order.

Basis outperforms plane-wave basis in phi^4 theory calculations.

Polynomials can be constructed from products of lower-order polynomials.

Abstract

We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint limits the two remaining independent momentum fractions to a triangle, for which the three momentum fractions act as barycentric coordinates. For three identical bosons, the wave function must be symmetric with respect to all three momentum fractions. Therefore, as a basis, we construct polynomials in two variables on a triangle that are symmetric with respect to the interchange of any two barycentric coordinates. We find that, through the fifth order, the polynomial is unique at each order, and, in general, these polynomials can be constructed from products of powers of the second and third-order polynomials. The use of such a basis is illustrated in a calculation of a light-front wave function in two-dimensional phi^4 theory; the polynomial basis performs much better than the plane-wave basis used in discrete light-cone quantization.