The Stueckelberg-Kibble Model as an Example of Quantized Symplectic Reduction
U. A. Wiedemann, N. P. Landsman
Abstract
Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory to the Stueckelberg-Kibble model. We explicitly construct the physical state space Hphys, which carries a massive representation of the Poincaré group. The longitudinal one-particle component arises from a particular Bogoliubov transformation of the five (unphysical) degrees of freedom one has started with. Our discussion exhibits the particular features of the proposed constrained quantization theory in great clarity.
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