Radial Lattice Quantization of 3D φ⁴ Field Theory

2020/06/28 by Richard C. Brower, George Fleming, George T. Fleming +7
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algorithm #Ansatz #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Curvature #Geometry #Lattice (music) #Lattice field theory #Mathematical physics #Mathematics #Monte Carlo method #Particle physics theoretical and experimental studies #Physics #Quantization (signal processing) #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum field theory #Quantum mechanics #hep-lat

paper · pdf · doi:10.1103/physrevd.104.094502

8 pages, 7 figures

arxiv created 2020/06/28 · openalex publication_date 2020/06/28 · arxiv updated 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The quantum extension of classical finite elements, referred to as quantum finite elements (\bf QFE)~\citeBrower:2018szu,Brower:2016vsl, is applied to the radial quantization of 3d φ⁴ theory on a simplicial lattice for the \mathbb R × \mathbb S² manifold. Explicit counter terms to cancel the one- and two-loop ultraviolet defects are implemented to reach the quantum continuum theory. Using the Brower-Tamayo~\citeBrower:1989mt cluster Monte Carlo algorithm, numerical results support the QFE ansatz that the critical conformal field theory (CFT) is reached in the continuum with the full isometries of \mathbb R × \mathbb S² restored. The Ricci curvature term, while technically irrelevant in the quantum theory, is shown to dramatically improve the convergence opening, the way for high precision Monte Carlo simulation to determine the CFT data: operator dimensions, trilinear OPE couplings and the central charge.

Citations

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