Quantum Group Schrödinger 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 $Δx=~(1-q)x$. Then, based on this, we develop the basic formalism of quantum group Schrödinger field theory in one spatial quantum dimension, and explicitly exhibit the $SU_{q}(2)$ covariant algebras satisfied by the $q$-bosonic and $q$-fermionic Schrödinger fields. We generalize this result to an arbitrary number of fields.