Quantum Fluctuations of Particles and Fields in Smooth Path Integrals
Takayasu Sekihara (KEK, Tsukuba)
TL;DR
This paper introduces a method for evaluating smooth Feynman path integrals using Gaussian-sum paths, accurately modeling quantum fluctuations of particles and gauge fields in Euclidean space.
Contribution
It develops a novel approach to smooth path integrals with Gaussian functions, enabling precise study of quantum fluctuations in particles and gauge fields.
Findings
Reproduces ground state properties of harmonic oscillator with high accuracy
Successfully evaluates quantum fluctuations of U(1) and SU(2) gauge fields in four dimensions
Provides a new computational framework for quantum field fluctuations
Abstract
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with exp(-S) by appropriate methods. The weighted smooth paths reproduce properties of the ground state of the harmonic oscillator in one dimension with high accuracy. Quantum fluctuations of U(1) and SU(2) gauge fields in four dimensions are also evaluated in our approach.
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