2008/08/08 by Julian Barbour, Barbour, Julian, Brendan Foster +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.0808.1223
openalex publication_date 2008/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem of Dirac that identifies primary first-class constraints as generators of physically irrelevant motions. We point out that certain assumptions on which Dirac based his argument do not hold for reparametrization invariant systems, and show that the primary Hamiltonian constraint of these systems does generate physical motion. We show explicitly how the argument fails for systems described by Jacobi's principle, which has a structure closely resembling that of general relativity. We defer discussion of general relativity and the implications for quantum gravity to a later paper.