Schrödinger representation and symplectic embedding of topological solitons

Abstract

Exploiting the SU(2) Skyrmion Lagrangian with second-class constraints associated with Lagrange multiplier and collective coordinates, we convert the second-class system into the first-class one in the Batalin-Fradkin-Tyutin embedding through the introduction of Stückelberg coordinates. In the enlarged phase space possessing the Stückelberg coordinates, we perform the "canonical" quantization to describe the Schrödinger representation of the SU(2) Skyrmion, so that we can assign via the homotopy class π4 (SU(2)) = Z2 half integers to the isospin quantum number for the solitons. The symplectic embedding and the Becchi-Rouet-Stora-Tyutin symmetries involved in the SU(2) Skyrmion are also investigated. © World Scientific Publishing Company.