This article is cited in 3 papers

Generalized Duality, Hamiltonian Formalism and New Brackets

S. Duplij

Theory Group, Nuclear Physics Laboratory, V. N. Karazin Kharkiv National University, 4 Svoboda Sq., Kharkiv 61022, Ukraine

Abstract: 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.

MSC: 37J05, 44A15, 49K20, 70H45

Received: 28.02.2013
Revised: 16.07.2013

Language: English

DOI: 10.15407/mag10.02.189

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