A Gauge Theory for Extra Dimension Detecting by Point Particle

‎From the viewpoint of‎ "‎extra dimension detecting,‎" ‎the phenomenon of the transition of the free point particle into 3d space is investigated‎. ‎In this way‎, ‎we formulate the problem using the second-class constrained system‎. ‎To investigate it using a gauge theoretical approach‎, ‎we use two methods to convert its two second-class constraints to first-class ones‎. ‎In symplectic embedding‎, ‎we construct a pair of scaler and vector gauge potentials‎, ‎which can be interpreted as interactions for detecting extra dimensions‎. ‎A Wess-Zumino variable appears as a new coordinate in potentials‎, ‎and the particle's mass plays the role of a globally conserved charge related to the constructed gauge theory for extra dimensions‎.