Modification of Dirac's method of Hamiltonian analysis for constrained systems

Journal Article · Fri Apr 15 04:00:00 EST 1983 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.27.1752· OSTI ID:5907924

Di Stefano, R

A slight modification of Dirac's method of Hamiltonian analysis for constrained systems is introduced. It leads to a verification of Dirac's conjecture that first-class secondary constraints are always symmetry generators in each of the counterexamples to that conjecture which have appeared in the recent literature. Those counterexamples associated with differentiable Hamiltonians are studied here; the cases involving nondifferentiable Hamiltonians will be considered separately. The relationship between the Lagrangian and Hamiltonian descriptions is studied in some detail and is used to motivate our calling the form of the secondary constraints derived via this modified method the natural form of the secondary constraints. Along the way we distinguish between symmetries of the Lagrangian (or Hamiltonian) and symmetries of the Euler-Lagrange (or Hamilton's) equations; we also distinguish between form and content invariance.

• Research Organization: Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, Long Island, New York 11794
• OSTI ID: 5907924
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 27:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
EQUATIONS OF MOTION
FUNCTIONS
HAMILTONIANS
LAGRANGIAN FUNCTION
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SYMMETRY
WAVE EQUATIONS