Unfolded Point Particle as a Field in Minkowski Space

TL;DR

This paper reformulates point-particle dynamics as a field theory using unfolded dynamics, providing a new geometric perspective and insights into symmetry realizations in lower-dimensional systems.

Contribution

It introduces a novel unfolded dynamics approach to describe point particles as fields, bridging higher-dimensional symmetries with lower-dimensional physical systems.

Findings

Reproduces conventional point-particle results

Provides a geometric interpretation of particle dynamics

Suggests a mechanism for symmetry realization in lower dimensions

Abstract

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.