  We consider the spectral stability of solitary wave solutions
\phi(x)e^{-i\omega t} to the nonlinear Dirac equation in any dimension. This
equation is well-known to theoretical physicists as the Soler model (or, in one
dimension, the Gross-Neveu model), and attracted much attention for many years.
We show that, generically, at the values of where the Vakhitov-Kolokolov
stability criterion breaks down, a pair of real eigenvalues (one positive, one
negative) appears from the origin, leading to the linear instability of
corresponding solitary waves.
  As an auxiliary result, we state the virial identities ("Pohozhaev theorem")
for the nonlinear Dirac equation.
  We also show that \pm 2\omega i are the eigenvalues of the nonlinear Dirac
equation linearized at \phi(x)e^{-i\omega t}, which are embedded into the
continuous spectrum for |\omega| > m/3. This result holds for the nonlinear
Dirac equation with any nonlinearity of the Soler form ("scalar-scalar
interaction") and in any dimension.
