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.