The Quantization of Geodesic Deviation

TL;DR

This paper introduces a method to quantize the geodesic deviation equation using canonical quantization, leading to generalized Klein-Gordon equations with potential applications in quantum wave packet spreading and quantum field theory.

Contribution

It presents a novel quantization approach for geodesic deviation, expanding the scope of quantized systems beyond traditional models.

Findings

Derivation of generalized Klein-Gordon equations from geodesic deviation

Potential applications in quantum wave packet analysis

Implications for one particle to many particle quantum systems

Abstract

There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations which generalize the Klein-Gordon equation. The resulting equations might have applications, and also show that entirely unexpected systems can be quantized. The possible applications of quantized geodesic deviation are to: i)the spreading wave packet in quantum theory, ii)and also to the one particle to many particle problem in second quantized quantum field theory.