  The paper shows that inhomogeneity of translation properties of condensate
leads to the interaction of local order parameter (OP) and its compensating
field which is similar to gauge fields in the field theory. Dynamic models were
considered in the theory of phase transitions to inhomogeneous state with local
translational symmetry, generalizing analogous models of static description
[A.Ya Braginsky, Phys. Rev. B66, 054202 (2002); A.Ya. Braginsky, Zh. Eksp.
Teor. Fiz. 132, 30 (2007)], where internal stress inevitably arises. In dynamic
models, symmetry-dependent stress tensor defines force, and continuous group
parameters of the local Landau potential are linked with the laws of
conservation and equations of continuity. Equations of continuity for momentum
in the present model are in agreement with the second Newton's law and result
from the equations of state, by analogy with equations of continuity for
current, obtained from Maxwell equations in electrodynamics. It is shown that
the principle of local homogeneity corresponds to the model of continuum with
fibering of space into locally homogeneous subspaces in each of its points,
resulting in the gauge model with minimal interaction in the Landau theory.
Phenomenological charge responsible for minimal interaction of an order
parameter (OP) and its compensating field linearly enters the expression for
momentum, that being in agreement with the principle of equivalence of masses.
Local Landau theory is consistent with ideas of quantum mechanics, because
condensate, in a small volume, has wave properties and describes the wave
function, which is transformed to local irreducible representation (IR) of the
subgroup of translations.
