Covariant entropic dynamics: from path independence to Hamiltonians and quantum theory

TL;DR

This paper develops a covariant entropic dynamics framework for scalar fields that derives quantum theory and Hamiltonian dynamics from path independence, emphasizing inference-based methods without traditional formalism.

Contribution

It introduces a covariant quantum entropic dynamics approach for scalar fields, deriving Hamiltonian structures and quantum theory solely from path independence principles.

Findings

Covariant quantum ED framework successfully derived.

Path independence leads to Hamiltonian dynamics.

Quantum potential's uniqueness is proven.

Abstract

Entropic Dynamics (ED) is an inference-based framework that seeks to construct dynamical theories of physics without assuming the conventional formalism --- the Hamiltonians, Poisson brackets, Hilbert spaces, etc. --- typically associated with physics. In this work we develop an ED of scalar fields that is both quantum and manifestly covariant. The framework for accomplishing this is inspired by the covariant methods of Dirac, Teitelboim, and Kuchar. In addition to the ostensible result of a covariant quantum ED, we also show how the covariance requirement of path independence proposed by Teitelboim is sufficient for a derivation of Hamiltonian dynamics and also provides a proof of uniqueness for the quantum potential that leads to quantum theory.