A novel Hamiltonian formulation of $1+1$ dimensional $\phi^4$ theory in Daubechies wavelet basis: momentum space analysis

TL;DR

This paper introduces a new Hamiltonian approach to 1+1 dimensional phi^4 theory using Daubechies wavelets in momentum space, enabling nonperturbative analysis of phase transitions.

Contribution

It develops a wavelet-based Hamiltonian formulation for quantum field theory, allowing natural infrared and ultraviolet truncations in a nonperturbative setting.

Findings

Demonstrates the nonperturbative phase transition in phi^4 theory

Uses Daubechies wavelets for momentum space basis

Provides a new framework for nonperturbative quantum field analysis

Abstract

We employ the wavelet formalism of quantum field theory to study field theories in the nonperturbative Hamiltonian framework. Specifically, we make use of Daubechies wavelets in momentum space. These basis elements are characterised by a resolution and a translation index that provides for a natural nonperturbative infrared and ultraviolet truncation of the quantum field theory. As an application, we consider the $\phi^4$ theory and demonstrate the emergence of the well-known nonperturbative strong-coupling phase transition in the $m^2>0$ sector.