Gauging of 1D-space translations for nonrelativistic matter - Geometric bags

We develop in a systematic fashion the idea of gauging 1D-space translation s with fixed Newtonian time For nonrelativistic matter (particles and field s). By starting with a nonrelativistic free theory we obtain its minimal ga uge invariant extension by introducing two gauge fields with a Maxwellian s elf interaction. We fix the gauge so that the residual symmetry group is th e Galilei group and construct a representation of the extended Galilei alge bra. The reduced N-particle Lagrangian describes geodesic motion in a (N-1) -dimensional (Pseudo-) Riemannian space. The singularity of the metric for negative gauge coupling leads in classical dynamics to the formation of geo metric bags in the case of two or three particles. The ordering problem wit hin the quantization scheme for N-particles is solved by canonical quantiza tion of a pseudoclassical Schrodinger theory obtained by adding to the cont inuum generalization of the point-particle Lagrangian an appropriate quantu m correction. We solve the two-particle bound state problem for both signs of the gauge coupling. At the end we speculate on the possible physical rel evance of the new interaction induced by the gauge fields. (C) 2000 Academi c Press.