Quantum Group Schr\"odinger Field Theory
Abstract
We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size x=~(1-q)x. Then, based on this, we develop the basic formalism of quantum group Schr\"odinger field theory in one spatial quantum dimension, and explicitly exhibit the SUq(2) covariant algebras satisfied by the q-bosonic and q-fermionic Schr\"odinger fields. We generalize this result to an arbitrary number of fields.
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