Principle of maximum caliber and quantum physics

MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and out of equilibrium. In this work, guided by the analogy of the formalism of MaxCal with that of the path integral formulation of quantum mechanics, we explore the extension of its applications to the realm of quantum physics, and show how the Lagrangians of both relativistic and nonrelativistic quantum fields can be built from MaxCal, with a suitable set of constraints. Related, the details of the constraints allow us to reinterpret the concept of inertia.

Figure 1

Points $a$ and $b$ can be connected by $N$ different paths, each designated by an index $i$. And each path's length is discretized in $n_i$ intervals, designated by index $j$.