Nonperturbative Matching Between Equal-Time and Lightcone Quantization

Abstract

We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of $\lambda {\varphi }^4$ 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.

23+9 pages, 10 figures; references added, discussion of perturbative matching clarified

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• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Critical behavior of the 2d scalar theory: resumming the ${\mathrm{N}}^8\mathrm{LO}$ perturbative mass gap
• Tadpoles and vacuum bubbles in light-front quantization
• Critical Coupling for Two-dimensional ${\varphi }^4$ Theory in Discretized Light-Cone Quantization