Unfolded Point Particle as a Field in Minkowski Space

Point-particle dynamics is reformulated as a field theory. This is achieved by using the unfolded dynamics approach that makes it possible to give dynamical interpretation to the concept of physical dimension which is 1 for a point particle in the $d$-dimensional space-time. The main idea for the description of a $k$-dimensional on-shell system in the $d$-dimensional space is to keep the evolution along $d-k$ dimensions off-shell or, alternatively, restrict it in a specific way respecting the compatibility conditions of the resulting unfolded system. The developed approach gives some hints how a non-linear realization of the symmetry $G$ of a larger-dimensional space in a lower-dimensional system can emerge from a geometrical realization on the fields in an appropriate $G$-invariant space. For the example of a relativistic point particle considered in this paper, $G$ is the Poincare group. The proposed general scheme is illustrated by simple examples that reproduce conventional results.