# An attractive $\phi^4$ theory in light-front coordinates

## TL;DR

This paper investigates an attractive $^4$ theory in 3+1 dimensions using light-front coordinates, revealing its asymptotic freedom, bound states, and non-perturbative renormalization effects.

## Contribution

It provides a non-perturbative analysis of the $^4$ theory in light-front coordinates, including renormalization, bound state wave functions, and energy bounds.

## Key findings

- The model is asymptotically free.
- Bound state wave functions are explicitly computed.
- A mean field bound for N-particle ground state energy is established.

## Abstract

We study an attractive $\phi^4$ interaction using Tamm-Dancoff truncation with light-front coordinates in $3+1$ dimensions. The truncated theory requires a coupling constant renormalization, we compute its $\beta$ function non-perturbatively, show that the model is asymptotically free, and find the corresponding Callan-Symanzik equations. The model supports bound states, we find the wave function for the ground state of the two-particle sector. We also give a bound for the $N$-particle ground state energy within a mean field approximation, including the corresponding result for the case of $2+1$ dimensions where the model does not require renormalization.