# Entropic Dynamics: Reconstructing Quantum Field Theory in Curved Space-time

## TL;DR

This paper extends the Entropic Dynamics approach to quantum field theory in curved space-time, providing an information-based, covariant formulation that aligns with classical Hamiltonian methods and addresses quantum divergences.

## Contribution

It introduces a covariant, entropic time framework for quantum fields in curved space-time, combining maximum entropy methods with classical covariant Hamiltonian formalisms.

## Key findings

- Derived Ehrenfest relations for fields in curved space-time
- Formulated a non-dissipative, foliation-invariant quantum dynamics
- Brief discussion on divergences in quantum field theory

## Abstract

The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kucha\v{r}, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.