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We develop a polynomial basis to be used in numerical calculations oflight-front Fock-space wave functions. Such wave functions typically depend onlongitudinal momentum fractions that sum to unity. For three particles, thisconstraint limits the two remaining independent momentum fractions to atriangle, for which the three momentum fractions act as barycentriccoordinates. For three identical bosons, the wave function must be symmetricwith respect to all three momentum fractions. Therefore, as a basis, weconstruct polynomials in two variables on a triangle that are symmetric withrespect to the interchange of any two barycentric coordinates. We find that,through the fifth order, the polynomial is unique at each order, and, ingeneral, these polynomials can be constructed from products of powers of thesecond and third-order polynomials. The use of such a basis is illustrated in acalculation of a light-front wave function in two-dimensional phi^4 theory; thepolynomial basis performs much better than the plane-wave basis used indiscrete light-cone quantization.

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