About non standard Lagrangians in cosmology

Dimitrijević, Dragoljub D.; Milošević, Milan

doi:10.1063/1.4748066

Cited by 14 publications

(5 citation statements)

References 10 publications

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“…The advantage of non-standard Lagrangians is that it can better describe nonlinear problems and plays an important role in non-conservative systems, dissipative systems, quantum field theory, etc. [25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

Zhang

Wang

2019

Symmetry

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Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved quantity of Mei symmetry in this system are presented and studied. Secondly, considering that a small disturbance is applied on the system, the differential equations of the disturbed motion are established, the definition of Mei symmetry and corresponding criterion are given, and the new adiabatic invariants led by Mei symmetry are proposed and proved. Examples also show the validity of the results.

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Section: Introductionmentioning

confidence: 99%

Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

Zhang

Wang

2019

Symmetry

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“…Nowadays, a series of results has been obtained for non-standard Lagrangians. Dimitrijevic and Milosevic [10] considered two classical examples with nonstandard Lagrangians in modern cosmological model, namely Dirac-Born-Infeld (DBI) Lagrangians in Tachyon field and P-adic string theory Lagrangians. El-Nabulsi [11][12][13][14][15][16] applied non-standard Lagrangians to Friedmann-Robertson-Walker spacetime and discussed its application in quantum mechanics by the modified Hamilton-Jacobi equation and Schrödinger equation, and generalized dynamical systems with higher order derivatives.…”

Section: Introductionmentioning

confidence: 99%

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

Song

Zhang

2017

Chinese Phys. B

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This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton principle based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both classical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

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“…Looking at the classical level, we can still choose another Lagrangian which will lead to the same equation of motion and would be more convenient [9,17,20]. However, one should be careful with the Lagrangians at the quantum level, which is a very old issue in general.…”

Section: Classically Equivalent Lagrangiansmentioning

confidence: 99%

“…In that case one can start with the (DBI) Lagrangian, for the spatially homogenous tachyon field [9,17] …”

Section: Tachyonic Lagrangianmentioning

confidence: 99%

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

Dimitrijević¹,

Djordjević²,

Milošević³

et al. 2014

AIP Conference Proceedings

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Abstract. We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional -classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking for a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.

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About non standard Lagrangians in cosmology

Cited by 14 publications

References 10 publications

Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

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