Working Paper Article Version 1 This version is not peer-reviewed

# A Probe of Micro Space-Time by the Study of Scalar Fields

Version 1 : Received: 6 October 2020 / Approved: 6 October 2020 / Online: 6 October 2020 (15:50:53 CEST)

How to cite: Deng, J.; Deng, M.; Fan, Q.; He, P. A Probe of Micro Space-Time by the Study of Scalar Fields. Preprints 2020, 2020100137 Deng, J.; Deng, M.; Fan, Q.; He, P. A Probe of Micro Space-Time by the Study of Scalar Fields. Preprints 2020, 2020100137

## Abstract

In this work, we try to find a way to describe the physical law of micro-world under the frame of a space-time theory. By introducing the scalar fields $\mathcal{D}\left( x\right)$ and $\zeta\left( x\right)$, we rewrite the action of conventional field theory and the Lagrangian describing the motion of the particle, where a modified space-time relation is obtained. To test the correctness of this attempt, we demonstrate the Klein-Gordon equation by the Hamilton-Jacobi method in four dimensional form and present a time delay for the ground state of hydrogen atom.

## Keywords

general relativity; scalar field; variational principle

## Subject

PHYSICAL SCIENCES, Acoustics

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