Maximum Caliber and quantum physics

TL;DR

This paper explores extending the MaxCal variational principle from classical to quantum physics, demonstrating how quantum Lagrangians can be derived from MaxCal and offering a new perspective on inertia.

Contribution

It introduces a novel approach to derive quantum field Lagrangians using MaxCal, bridging classical variational principles with quantum mechanics.

Findings

Quantum Lagrangians can be constructed from MaxCal with appropriate constraints.

MaxCal provides a new interpretation of inertia in quantum systems.

The formal analogy between MaxCal and path integral formulation is established.

Abstract

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 non-relativistic quantum fields can be built from MaxCal, with a suitable set of constraints. Related, the details of the constraints allow us to find a new interpretation of the concept of inertia.