# A Framework for Non-linear Time Evolution and Field Theories on State-Dependent Geometries

## TL;DR

This paper proposes a novel framework for non-linear time evolution in quantum mechanics and extends it to models of dynamical geometry and quantum field theory on state-dependent geometries, offering new perspectives on quantum dynamics.

## Contribution

It introduces a unified framework for non-linear quantum evolution and models of dynamical geometry, bridging quantum mechanics and quantum field theory on variable geometries.

## Key findings

- Derived simple toy models of dynamical geometry on finite graphs
- Proposed a non-linear quantum field theory on state-dependent geometries
- Established a foundation for further exploration of non-linear quantum dynamics

## Abstract

We introduce a framework for non-linear time evolution in quantum mechanics as a natural non-linear generalization of the Schrodinger equation. Within our framework, we derive simple toy models of dynamical geometry on finite graphs. Along similar lines we also propose a model of non-linear quantum field theory on spaces with state-dependent geometry.