Generalized collective coordinate quantization of solitons with topological terms

For the solitons of the theory including topological terms, the standard collective coordinate quantization does not construct the proper low energy effective theory. In the presence of topological terms, zero modes are classified into three groups: dynamical zero modes with constant velocity, cyclotron zero modes in a circular orbit, and static constraint zero modes. According to the mode expansion, the topological term contributes to the moduli metric of the dynamical zero modes. In addition, constraint zero modes do not have the kinetic term and produce constraints that strongly restrict the spectrum instead. In this paper, we propose a generalized collective coordinate quantization method and apply it to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> Skyrmion with the Wess-Zumino-Witten term. We find five constraints. These reproduce the results of Cherman [The collective quantization of three-flavored skyrmions revisited, ], eliminating all the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>S</e:mi> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>3</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> multiplets except the nucleon octet and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi mathvariant="normal">Δ</i:mi> </i:math> baryon decuplet from the collective coordinate part of the spectrum.