Introduction to spherical field theory

TL;DR

Spherical field theory is a novel non-perturbative approach that simplifies quantum field theories into coupled one-dimensional systems, enabling numerical solutions demonstrated on 2D phi^4 theory.

Contribution

Introduces spherical field theory as a new non-perturbative method using spherical partial wave expansion for quantum field analysis.

Findings

Successfully applied to 2D phi^4 theory

Reduces complex theories to coupled 1D systems

Provides a numerical framework for quantum field analysis

Abstract

Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional systems. The coupled one-dimensional systems are then converted to partial differential equations and solved numerically. We demonstrate the methods of spherical field theory by analyzing Euclidean phi^4 theory in two dimensions.