Nonperturbative Matching Between Equal-Time and Lightcone Quantization

TL;DR

This paper explores the nonperturbative relationship between lightcone and equal-time quantization in 2D $bbbphi^4$ theory, proposing a method to relate their parameters via Borel resummation and validating it with numerical comparisons.

Contribution

It introduces a nonperturbative map between bare parameters in lightcone and equal-time quantization, derived from perturbation theory and validated through numerical Hamiltonian truncation.

Findings

The nonperturbative map can be obtained from Borel resummation of ET perturbation theory.

Numerical tests show consistency between LC and ET computed quantities using the proposed map.

Naive nonperturbative extensions of perturbative matching fail, but the proposed method succeeds.

Abstract

We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of $\lambda \phi^4$ theory in $d=2$. We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.