2D(1+1) Quantum Gravity. Gravitational Quantum Stationary Hamilton-Jacobi Equation

Abstract

In the present article, we construct a 2D formulation of quantum gravity in the framework of a deterministic theory. In this context, a Quantum stationary Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in the presence of a gravitational field. We show that this equation reduces to the Quantum stationary Hamilton- Jacobi equation when the gravitational field is not present in the 2D time-space. As a second step, we introduce the quantum gravitational Lagrangian for the quantum motion of a particle moving in the presence of a gravitational field. We, deduce the relationship between the gravitational quantum conjugate momentum and the velocity of the particle.

Latex, no figures, 19 pages

References in corpus (4)

• Families of exact solutions of a 2D gravity model minimally coupled to electrodynamics
• Relativistic Quantum Newton's Law and photon trajectories
• Nodes in the Relativistic Quantum Trajectories and Photon's Trajectories
• The Relativistic Quantum Stationary Hamilton Jacobi Equation for Particle with Spin 1/2