General relativity as a fully singular Lagrange system

• Main Author: Tao Mei
• Format: Article
• Language: English
• Published: Elsevier 2020-06-01
• Series: Results in Physics
• Subjects: General relativity; Coordinate conditions; Vierbein; Hamiltonian representation; Fully singular Lagrange system; Canonical quantization
• Online Access: http://www.sciencedirect.com/science/article/pii/S2211379719327871

Based on properties of six special gauge-fixing terms of tetrad, some coordinate conditions are presented, which lead to that all second time derivative terms of tetrad in Einstein equation are removed when general relativity is expressed by tetrad formulation; this result does not contradict the well known fact that the number of propagating degrees of freedom in general relativity equals two. Under these coordinate conditions, we prove that general relativity becomes a fully singular Lagrange system in terms of the vierbein forms of the action and the Hamiltonian representation of the system consisting of gravitation-Dirac-scalar-Maxwell fields; some properties of such system are discussed. By introducing six new variables to replace induced spatial metric, some properties of the coordinate conditions are presented, besides, the operator ordering of all the terms in the Hamiltonian and the Diffeomorphism constraints are fully determined after realizing canonical quantization of general relativity.