Hamilton–Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton–Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamilto...

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Bibliographic Details
Published in:Annals of physics 2008-03, Vol.323 (3), p.527-547
Main Authors: Bertin, M.C., Pimentel, B.M., Pompeia, P.J.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Comparative studies
COORDINATES
First order actions
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
Hamilton–Jacobi formalism
Higher order derivatives
LAGRANGIAN FUNCTION
Mathematics
Physics
QUANTIZATION
Singular systems
Theory
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Summary:In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton–Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2007.11.003