Grand Canonical Ensembles, Multiparticle Wave Functions, Scattering Data, and Lattice Field Theories

Area of Science:

• Quantum Field Theory
• Statistical Mechanics
• Lattice Gauge Theory

Background:

• Studying quantum field theories (QFTs) at finite density and low temperatures presents challenges, particularly the complex action problem at nonzero chemical potential.
• Traditional methods for obtaining scattering data often struggle with nonperturbative regimes and complex systems.

Purpose of the Study:

• To demonstrate a novel approach for extracting scattering data from QFTs by analyzing systems at finite density and low temperatures.
• To utilize exact dualizations of lattice models to overcome limitations of traditional methods and gain insights into two-particle interactions.

Main Methods:

• Formulating lattice models that can be exactly dualized to theories of conserved charge fluxes.
• Employing dual Monte Carlo simulations on these dual theories to interpret particle world lines and extract wave function data.
• Analyzing critical chemical potential values and two-particle wave functions in fixed particle number sectors.

Main Results:

• Successfully extracted scattering phase shifts for the two-dimensional O(3) model at nonzero chemical potential and finite volume.
• Demonstrated that both critical chemical potential values and direct wave function analysis yield accurate scattering phase shifts.
• Achieved excellent agreement between the novel method's results and exact solutions for the studied model.

Conclusions:

• The proposed method provides a viable and accurate way to obtain scattering data for QFTs, particularly in challenging nonperturbative regimes.
• The dualization technique effectively bypasses the complex action problem and offers a particle world line interpretation.
• The approach shows broad applicability and generality for extracting fundamental QFT information.