Abstract
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The observables are invariant with respect to spatial diffeomorphisms which preserve the observer. The limited residual spatial gauge freedom is studied and fully understood. A full canonical analysis of the observables is presented: we analyze their variations, Poisson algebra and discuss their dynamics. Lastly, the observables are used to solve the vector constraint, which triggers a possible considerable reduction of the degrees of freedom of general relativistic theories.
Highlights
Be the mathematical structure best suited to be endowed with geometry and turned into a spacetime
We present a new scheme of defining invariant observables for general relativistic systems
Given a physical general relativistic system described by fields φ1, . . . , φn, it is only the diffeomorphism invariant information that has a physical meaning
Summary
We consider canonical gravity coupled to some matter fields. The theory consists of a 3-manifold Σ and canonically conjugate pairs of fields defined thereon: a 3-metric tensor qij and its momentum pij, remaining fields φα and πα, α = 1, . Each set of fields (q, p, φα, πα) is a point in the kinematical phase space Γ of the considered theory. The. In section 5.2, physical points of Γ are selected, as those which satisfy the ArnowittDeser-Misner (ADM [9]) vector constraints Ci(σ) = 0 which in the spacetime approach generate the diffeomorphisms of the Cauchy surface, and in the phase space Γ generate the induced action of the diffeomorphisms of Σ
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