We propose a lattice field theory formulation which overcomes some
fundamental difficulties in realizing exact supersymmetry on the lattice. The
Leibniz rule for the difference operator can be recovered by defining a new
product on the lattice, the star product, and the chiral fermion species
doublers degrees of freedom can be avoided consistently. This framework is
general enough to formulate non-supersymmetric lattice field theory without
chiral fermion problem. This lattice formulation has a nonlocal nature and is
essentially equivalent to the corresponding continuum theory. We can show that
the locality of the star product is recovered exponentially in the continuum
limit. Possible regularization procedures are proposed.The associativity of the
product and the lattice translational invariance of the formulation will be
discussed.Comment: 14 pages, Lattice2017 Proceeding
