This article is cited in 2 scientific papers (total in 2 papers)
Generalized Duality, Hamiltonian Formalism and New Brackets
Theory Group, Nuclear Physics Laboratory, V. N. Karazin Kharkiv National University, 4 Svoboda Sq., Kharkiv 61022, Ukraine
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar to the Poisson gauge theory; 3) can be treated as the many-time classical dynamics. A generalization of the Legendre transform to the zero Hessian case is done by using the mixed (envelope/general) solution of the multidimensional Clairaut equation. The equations of motion are written in the Hamilton-like form by introducing new antisymmetric brackets. It is shown that any classical degenerate Lagrangian theory is equivalent to the many-time classical dynamics. Finally, the relation between the presented formalism and the Dirac approach to constrained systems is given.
Key words and phrases:
Dirac constraints, nonabelian gauge theory, degenerate Lagrangian, Hessian, Legendre transform, multidimensional Clairaut equation, gauge freedom, Poisson bracket, many-time dynamics.
PDF file (296 kB)
MSC: 37J05, 44A15, 49K20, 70H45
S. Duplij, “Generalized Duality, Hamiltonian Formalism and New Brackets”, Zh. Mat. Fiz. Anal. Geom., 10:2 (2014), 189–220
Citation in format AMSBIB
\paper Generalized Duality, Hamiltonian Formalism and New Brackets
\jour Zh. Mat. Fiz. Anal. Geom.
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This publication is cited in the following articles:
Walker M.L., Duplij S., “Cho-Duan-Ge Decomposition of Qcd in the Constraintless Clairaut-Type Formalism”, Phys. Rev. D, 91:6 (2015), 064022
Duplij S., “Formulation of Singular Theories in a Partial Hamiltonian Formalism Using a New Bracket and Multi-Time Dynamics”, Int. J. Geom. Methods Mod. Phys., 12:1 (2015), 1550001
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