**
Below is the ascii version of the abstract for 97-335.
The html version should be ready soon.**Luis Gonzalez-Mestres
Lorentz symmetry violation and very high-energy cross sections
(20K, LaTex)
ABSTRACT. We discuss the implications of a recently proposed pattern of Lorentz
symmetry violation on very high-energy cross sections. As a consequence
of the breaking of local Lorentz invariance by the introduction of a
fundamental length, $a$ , the kinematics is modified and the properties
of final states are fundamentally different in collider-like (two
incoming particles with equal, opposite momenta with respect to the
vacuum rest frame) and fixed-target (one of the incoming particles at
rest with respect to the vacuum rest frame) situations. In the first
case, the properties of the allowed final states are similar to
relativistic kinematics, as long as the relevant wave vectors are much
smaller than the critical wave vector scale $a^{-1}$ . But, if one of
the incoming particles is close to rest in the vacuum rest frame,
energy conservation reduces the final-state phase space at very high
energy and can lead to a sharp fall of cross sections starting at
incoming-particle wave vectors well below the inverse of the
fundamental length. Then, the Froissart bound may cease to be relevant,
as total cross sections seem to become much smaller than it would be
allowed by local, Lorentz-invariant, field theory. Important
experimental implications of the new scenario are found for cosmic-ray
astrophysics and for very high-energy cosmic rays reaching the earth.