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On the energy momentum dispersion in the lattice regularization
For a free scalar boson field and for U(1) gauge theory finite volume
(infrared) and other corrections to the energy-momentum dispersion in the
lattice regularization are investigated calculating energy eigenstates from the
fall off behavior of two-point correlation functions. For small lattices the
squared dispersion energy defined by is in both cases
negative ( is the Euclidean space-time dimension and the
energy of momentum eigenstates). Observation of has
been an accepted method to demonstrate the existence of a massless photon
() in 4D lattice gauge theory, which we supplement here by a study of
its finite size corrections. A surprise from the lattice regularization of the
free field is that infrared corrections do {\it not} eliminate a difference
between the groundstate energy and the mass parameter of the free
scalar lattice action. Instead, the relation is
derived independently of the spatial lattice size.Comment: 9 pages, 2 figures. Parts of the paper have been rewritten and
expanded to clarify the result