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Nonperturbative Infrared Finiteness in a Superrenormalizable Scalar Quantum Field Theory.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • Mathematical Physics

Background:

  • Investigating the infrared (IR) behavior of superrenormalizable quantum field theories.
  • A bare mass is necessary for the theory to be massless at the quantum level.
  • Perturbation theory reveals ambiguities in the critical mass due to IR divergences.

Purpose of the Study:

  • To examine the infrared (IR) behavior of a three-dimensional superrenormalizable quantum field theory.
  • To test the conjecture that superrenormalizable theories are nonperturbatively IR finite.
  • To determine if the coupling constant acts as an IR regulator.

Main Methods:

  • Lattice perturbation theory to analyze critical mass behavior at two loops.
  • Markov Chain Monte Carlo simulations of the lattice-regularized theory.
  • Frequentist and Bayesian data analysis, alongside effective theory considerations.

Main Results:

  • The critical mass in lattice perturbation theory diverges logarithmically at two loops.
  • Evidence gathered supports the conjecture of nonperturbative IR finiteness in superrenormalizable theories.
  • The coupling constant appears to function as an IR regulator.

Conclusions:

  • Superrenormalizable quantum field theories exhibit nonperturbative infrared finiteness.
  • The coupling constant effectively regulates infrared divergences.
  • The study provides strong evidence for theoretical conjectures using computational and analytical methods.