  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 introduction of the St\"uckelberg coordinates. In this
extended phase space we construct the "canonical" quantum operator commutators
of the collective coordinates and their conjugate momenta to describe the
Schr\"odinger representation of the SU(2) Skyrmion, so that we can define
isospin operators and their Casimir quantum operator and the corresponding
eigenvalue equation possessing integer quantum numbers, and we can also assign
via the homotopy class $\pi_{4}(SU(2))=Z_{2}$ half integers to the isospin
quantum number for the solitons in baryon phenomenology. Different from the
semiclassical quantization previously performed, we exploit the "canonical"
quantization scheme in the enlarged phase space by introducing the
St\"uckelberg coordinates, to evaluate the baryon mass spectrum having global
mass shift originated from geometrical corrections due to the $S^{3}$ compact
manifold involved in the topological Skyrmion. Including ghosts and
anti-ghosts, we also construct Becci-Rouet-Stora-Tyutin invariant effective
Lagrangian.

High Energy Physics - Theory