2003/02/28 by Olivera Miskovic, Olivera Mišković, Jorge Zanelli · 61 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Dynamical systems theory #Geometry #Hamiltonian (control theory) #Hamiltonian system #Lagrangian #Mathematical analysis #Mathematical optimization #Mathematics #Multilinear map #Nonlinear Waves and Solitons #Nonlinear system #Numerical methods for differential equations #Physics #Pure mathematics #Quadratic equation #Quantization (signal processing) #Quantum mechanics #Regularization (linguistics) #Rotation formalisms in three dimensions #hep-th
paper · pdf · doi:10.1063/1.1601299
published in Journal of Mathematical Physics 44(9), 3876-3887 (American Institute of Physics) · 14 pages, no figures, references added. Final version for J. Math. Phys
openalex publication_date 2003/08/21 · arxiv created 2003/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the constraint surface into two fundamental types. If the irregular constraints are multilinear (type I), then it is possible to regularize the system so that the Hamiltonian and Lagrangian descriptions are equivalent. When the constraints are power of a linear function (type II), regularization is not always possible and the Hamiltonian and Lagrangian descriptions may be dynamically inequivalent. It is shown that the inequivalence between the two formalisms can occur if the kinetic energy is an indefinite quadratic form in the velocities. It is also shown that a system of type I can evolve in time from a regular configuration into an irregular one, without any catastrophic changes. Irregularities have important consequences in the linearized approximation to nonlinear theories, as well as for the quantization of such systems. The relevance of these problems to Chern–Simons theories in higher dimensions is discussed.