Mollifying Quantum Field Theory or Lattice QFT in Minkowski Spacetime and Symmetry Breaking

TL;DR

This paper introduces mollification techniques to smooth oscillatory functions in numerical Quantum Field Theory, aiming to improve calculations involving phase transitions, imaginary chemical potentials, and Minkowski spacetime lattice QFT.

Contribution

It applies the mathematical concept of mollification to numerical QFT, a novel approach that could enhance computational stability and accuracy in challenging oscillatory integrals.

Findings

Mollification effectively smooths highly oscillatory exponentials.

Potential improvements in calculating phase transitions and Minkowski spacetime lattice QFT.

Provides a new computational tool for complex quantum field calculations.

Abstract

This work develops and applies the concept of mollification in order to smooth out highly oscillatory exponentials. This idea, known for quite a while in the mathematical community (mollifiers are a means to smooth distributions), is new to numerical Quantum Field Theory. It is potentially very useful for calculating phase transitions [highly oscillatory integrands in general], for computations with imaginary chemical potentials and Lattice QFT in Minkowski spacetime.