  The coupling of lattice deformations to the low energy electronic excitations
of Dirac matter involve novel types of electron--phonon couplings as the
celebrated elastic gauge fields first analyzed in graphene. In the continuum
low energy approach, lattice deformations coupling to the electronic degrees of
freedom are characterized by the (symmetric) strain tensor defined in
elasticity theory. We review these couplings in Weyl semimetals and examine the
coupling of electronic excitations to the antisymmetric part of the deformation
gradient tensor associated to rotational strain. The new couplings, absent in
the two dimensional materials, have important physical implications: they give
rise to new elastic gauge fields, contribute to the deformation potential, tilt
the cones and generate new pseudo--Zeeman couplings.
