  There are different physics-based approaches for analysing pedestrian
movement. Physics-based methods like statistical mechanics-based models apply
the laws of physics to drive equations for analysing crowd behaviour. This
paper will introduce a physics-based approach based on field theory as a new
tool for crowd analysis to determine governing differential equations.
Formulating the pedestrian movement with differential equations has a primary
advantage for data assimilation techniques because some of these methods only
work with models with analytical transition functions, which are obtained by
incorporating a field approach. Furthermore, the field approach provides more
generality since the field could be any scalar field. Several Lagrangians are
presented in this work, and the primary purpose was to lay the groundwork for
this new type of thinking. Furthermore, as pedestrian movement is mainly
unregulated, the approach presented in the paper can be valuable for future
development since the Lagrangian could be explicitly obtained for pedestrian
movement spaces such as train stations and shopping malls. Finally, we discuss
a general approach for predicting the action and how neural networks might play
a role, which brings more flexibility and extendibility to our approach.
