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

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 ${\varphi }^4$ theory illustrates the use of these polynomials.

arXiv comment11 pages, 1 figure, RevTeX 4.1

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Cited by in corpus (11)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Nonperturbative light-front Hamiltonian methods
• A Conformal Truncation Framework for Infinite-Volume Dynamics
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• Two-dimensional light-front ${\varphi }^4$ theory in a symmetric polynomial basis
• Longitudinal dynamics for mesons on the light cone
• Light-front ${\varphi }_2^4$ theory with sector-dependent mass
• Light-front ${\varphi }_{1+1}^4$ theory using a many-boson symmetric-polynomial basis
• High Resolution Nonperturbative Light-Front Simulations of the True Muonium Atom
• Symmetry breaking in light-front ${\varphi }^4$ theory
• Nonperturbative True Muonium on the Light Front with TMSWIFT