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

Area of Science:

• Quantum Field Theory
• Computational Physics

Background:

• Light-front wave functions are crucial for describing relativistic bound states.
• Existing numerical methods, like plane-wave bases, face limitations in efficiency and accuracy.

Purpose of the Study:

• To develop a new, efficient polynomial basis for light-front Fock-space wave function calculations.
• To improve the numerical treatment of symmetric wave functions for identical particles.

Main Methods:

• Constructed a unique polynomial basis in barycentric coordinates on a triangle, ensuring symmetry for three identical bosons.
• Demonstrated the basis's construction from lower-order polynomials.
• Applied the basis to a two-dimensional phi(4) theory calculation.

Main Results:

• The developed polynomial basis is unique up to the fifth order.
• The basis significantly outperforms the conventional plane-wave basis.
• Numerical calculations show improved efficiency and accuracy.

Conclusions:

• The novel polynomial basis provides a more effective tool for numerical calculations of light-front wave functions.
• This approach enhances the study of quantum systems in relativistic frameworks.
• The method shows promise for advancing discrete light-cone quantization techniques.