  We study the effect of Rashba spin-orbit coupling (SOC) on the charge and
spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal.
As electrons in a quasi-1D Wigner crystal can move in the transverse direction,
SOC cannot be gauged away in contrast to the pure 1D case. We show that for
weak SOC, a partial gap in the spectrum opens at certain ratios between density
of electrons and the inverse Rashba length. We present how the low-energy
branch of charge degrees of freedom deviates due to SOC from its usual linear
dependence at small wave vectors. In the case of strong SOC, we show that spin
sector of a Wigner crystal cannot be described by an isotropic
antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground
state of neighboring electrons is mostly a triplet state. We present a new spin
sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.
