Quantum geometric phase with initial state index dependent on space-time curvature

TL;DR

This paper presents a novel method for generating quantum geometric phases by linking the initial state index to space-time curvature, revealing a deep connection to Einstein's gravitational equations in the adiabatic limit.

Contribution

It introduces an initial state setup dependent on space-time curvature that relates quantum geometric phases to Einstein's equations, a new conceptual link in quantum gravity.

Findings

Quantum geometric phase generation depends on space-time curvature.

Schrödinger equation aligns with Einstein's gravitational equations in the adiabatic limit.

Initial state index dependence offers a new perspective on quantum-gravity interactions.

Abstract

We introduce a new way of generating the quantum geometric phase by making the initial base state index dependent on space-time curvature. We prove that the resulting Schr\"odinger equation is identical to the trace form of the Einstein gravitational field equations when we are in the adiabatic approximation. This particular initial condition was proposed in a previous work by the author.