Abstract
We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of λϕ4 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.
Highlights
Operators appear in Heff, at which point their coefficients can be fixed in principle in terms of physical observables
We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of λφ4 theory in d = 2
We argue that they are the same theory nonperturbatively, and that the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap
Summary
In a heroic effort, the perturbative coefficients of both the vacuum energy density Λ(λ) and the mass gap μgap(λ) have recently been computed to O(λ8) in this theory [19] In defining the Lagrangian (2.1) in terms of normal-ordered operators, we subtracted off the divergent contributions to the vacuum energy and bare mass, which depend on m2. We computed the Hamiltonian in LC quantization in a basis of operators with dimension up to ∆max, and we substituted these matrix elements into the time-independent perturbation theory formula for the singleparticle state energy..
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