  We develop the theory of transportation and localization of a transparent
dielectric spherical particle with the gradient forces in the interference
field of orthogonally directed standing laser waves $E_z (\cos kz)$ and $E_x
(\cos kx)$. It is shown that, when the waves $E_z$ and $E_x$ are coherent, the
interference radiation field contains two harmonic components with the periods
$\Lambda_0=\pi/k$ and $\Lambda_\Delta=\pi/(k \sin (\pi/4))$. The amplitudes of
the gradient force components depend on the ratio of the particle radius $R$ to
the modulation periods due to inhomogeneity of radiation in the particle volume
and are given by the Bessel functions $J_{3/2} (2 \pi R/\Lambda_0)$ and
$J_{3/2} (2 \pi R/\Lambda_\Delta)$. We find the critical particle radii $R_0$
and $R_\Delta=\sqrt{2} R_0$ defined by the Bessel functions zeros and
corresponding to the vanishing components of the gradient forces. In
particular, for the radiation with the wavelength $\lambda_0=1.064$ {\mu}m and
a particle in water, the smallest critical radii are $R_0=0.286$ $\mu$m and
$0.492$ {\mu}m and $R_\Delta=0.404$ $\mu$m and $0.696$ $\mu$m, respectively.
For a number of special cases, we obtain the analytical solutions of the Newton
equations and the particle trajectories that depend on the ratio of wave
intensities and the particle radius. The results can be used to study the
dynamics of the "optical assembly" of a two-dimensional particles matrix which
behaves as a molecular crystal.
