Shortcut for constructing any Lagrangian from its equations of motion

Hojman, R.; Hojman, Sergio A.; Sheinbaum, Julio

doi:10.1103/physrevd.28.1333

Cited by 23 publications

(17 citation statements)

References 5 publications

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“…It is important to remark that this method is useful for both second-order and first-order differential equations [1]. For further details the reader is exhorted to review [1,19] and the references therein.…”

Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

“…which is the general effective potential for equation (1) given the choice (19) for the kinetic energy. In summary, we have presented in this Letter a novel way to provide both variational and effective potential formulations for general SPDEs with arbitrary noise function.…”

Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

“…This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. The inverse problem of variational calculus have been used by Hojman et al [1] in the study of systems associated with first and second order deterministic differential equations. The propoused method permits to obtain all the dynamical infomation of the system allowing the quantization in terms of conserved quantities prescibed for the differential equation.…”

mentioning

confidence: 99%

“…The inverse problem of variational calculus have been used by Hojman et al [1] in the study of systems associated with first and second order deterministic differential equations. The propoused method permits to obtain all the dynamical infomation of the system allowing the quantization in terms of conserved quantities prescibed for the differential equation.…”

mentioning

confidence: 99%

“…We will use in this Letter the Hojman et al [1] proceedure, which enables to construct the Lagrangean for any regular mechanical system as a linear combination of its own equations of motion. This particular construction is much wider than the traditional definition L = T − V , which is only true when the "forces" involved are derivable from position-dependent potentials, therefore it may be used for general nonconservative systems.…”

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confidence: 99%

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Variational and potential formulation for stochastic partial differential equations

Munoz¹,

Ojeda²,

Sierra³

et al. 2006

J. Phys. A: Math. Gen.

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There is recent interest in finding a potential formulation for Stochastic Partial Differential Equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this Letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al. method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangean, and that this potential is able to reproduce all the dynamics of the system, once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. The inverse problem of variational calculus have been used by Hojman et al. [1] in the study of systems associated with first and second order deterministic differential equations. The propoused method permits to obtain all the dynamical infomation of the system allowing the quantization in terms of conserved quantities prescibed for the differential equation. On the other hand, a variational formalism has been devised by Gambár and Márkus (see for example [2, 3, 4]) as groundwork for proposing a field theory for nonequilibrium thermodynamical systems, giving valuable information about the entropy in terms of current density and thermodynamic forces. Effective actions can be found by means of the Martin-Siggia-Rose formalism [5], a perturbative procedure that makes use of both physical and "conjugate" (auxiliary) fields. Also, Hochberg et al. have proposed in a series of papers [6,7,8] a "direct" approach, finding effective actions and potentials for SPDEs using a functional integral formalism similar in structure to those of quantum field theory. Last year Ao [9] has reported a worth consulting novel approach for constructing potentials associated with first order SPDEs. All this efforts conduct to the idea that the variational formalism, in its direct or inverse form, could be the mathematical mechanism with the necessary tools for exploring the inherent dynamics of physical, biological and chemical systems. In particular, structural development in cosmology and biology, pattern-formation, symmetry breaking, *

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Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

Section: The Hojman Et Al Methods Enables Us To Writementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Variational and potential formulation for stochastic partial differential equations

Munoz¹,

Ojeda²,

Sierra³

et al. 2006

J. Phys. A: Math. Gen.

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Variational principles for nonpotential operators

Filippov¹,

Savchin²,

Shorokhov³

1994

J Math Sci

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Equivalent Lagrangians in classical field theory

Hojman

Shepley

1986

Found Phys

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Two Lagrangians L and L' are equivalent if the equations of motion derived from them have the same set of solutions. In that case. a matrix A may be defined which has the property that the trace of any analytic function of A is a constant of the motion. We extend this trace theorem to the case of classical field theory and discuss some of the implications for quantum theory and for procedures for finding equivalent Lagrangians.

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Shortcut for constructing any Lagrangian from its equations of motion

Cited by 23 publications

References 5 publications

Variational and potential formulation for stochastic partial differential equations

Variational and potential formulation for stochastic partial differential equations

Variational principles for nonpotential operators

Equivalent Lagrangians in classical field theory

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