1996/12/15 by Josep M. Pons, J. M. Pons, Donald Salisbury +2 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant Hamiltonian field theory #Covariant transformation #Diffeomorphism #Gauge theory #Geometry #Hamiltonian (control theory) #Hamiltonian system #Lagrangian #Legendre transformation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Quantum mechanics #Rotation formalisms in three dimensions #Spacetime #Theoretical physics #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.55.658
12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev. D
arxiv created 1996/12/15 · openalex publication_date 1997/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.