How commutators of constraints reflect the spacetime structure

摘要: Abstract The structure constants of the “algebra” constraints a parametrized field theory are derived by simple geometrical argument based exclusively on path independence dynamical evolution; change in canonical variables during evolution from given initial surface to final must be independent particular sequence intermediate used actual evaluation this change. requirement also implies that will propagate consistently only data such Hamiltonian vanishes. vanishing arises because metric is variable rather than c-number. It not assumed can solved express four momenta terms remaining variables. shown signature spacetime read off commutator two at different points. analysis applies equally well irrespective whether prescribed Riemannian background or it determined itself as general relativity. In former case commutators imposes consistency conditions for which states defined arbitrary spacelike surfaces; whereas, later provides existence spacetime— “embeddability” ensure three-geometry viewed “motion” three-dimensional cut four-dimensional hyperbolic signature.