Space-time symmetries for theories with extended objects

Abstract

We examine the implications of space-time symmetries for quantum field theories with extended objects. It is shown that the existence of the quantum coordinate (collective coordinate) $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ is a direct consequence of the canonical formulation of translational invariance. In 1 + 1 dimensions, Lorentz invariance fixes uniquely the structure of the theory in the no-particle sector. If the tree approximation is used, the structure of the one-particle sector is also uniquely determined. Finally, the techniques developed in this paper allow us to deduce that nonspherically symmetric objects in three dimensions require additional quantum coordinates besides $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$.