1201.0055 (Takayasu Sekihara)

New Approach to Continuum Path Integrals for Particles and Fields    [PDF]

Takayasu Sekihara

An approach to approximate evaluation of the continuum 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 smooth functions and are weighted with exp(-S) by the Metropolis method. The weighted smooth paths reproduce properties of the ground state of the harmonic oscillator in one dimension with 80-90% accuracy. Our approach is applied to quantum field theories and quantum fluctuations of U(1) and SU(2) gauge fields in four dimensions respectively provide the Coulomb force and confining linear potential at qualitative levels via the Wilson loops. Behavior of the string tension for the SU(2) linear potential is consistent with the renormalization group prediction.

View original: http://arxiv.org/abs/1201.0055