On the Schrödinger equation for the free gravitational field

2013/07/30 by Alexei M. Frolov, Frolov, Alexei M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1307.7900

arxiv created 2013/07/30 · arxiv updated 2013/07/31

Abstract

The Hamiltonian of the metric General Relativity derived in our earlier study (Gravitation, \bf 17, 314 - 323 (2011)) is analyzed by the methods of Matrix Quantum Mechanics. This Hamiltonian is a quadratic function of the momenta π^mn conjugate to the spatial components g_mn of the metric tensor g_αβ. The Hamiltonian is reduced to the new form which is more convenient to derive the Schrödinger equation for the free gravitational field. In turn, this Schrödinger equation is used to study possible motions of the free gravitational field(s). In particular, it is shown that harmonic oscillations of the free gravitational field, or harmonic gravitational waves, cannot be observed as an actual motion of this field. We also investigate the internal structure of the solitary gravitational wave.

Related

• On the Hamilton approach for the metric GR
• Free gravitational field in the metric gravity as a Hamilton system
• The Schrödinger equation for a spherically symmetric system, its structure and solutions
• Reduction of the canonical Hamiltonian of the metric GR to its natural form
• Constants of the Motion in a Gravitational Field and the Hamilton-Jacobi Function