  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 Gauss 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 more than about 90 % accuracy, and the accuracy gets higher by
using smaller width of the Gauss functions. 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. Distributions of large
values of gauge fields are found to be suppressed at least exponentially.
