Clebsch parameterization from the symplectic point of view

Neves, C.; Oliveira, W.

doi:10.1016/j.physleta.2003.12.039

Cited by 19 publications

(18 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, in Ref. [39] this kind of problem was solved. On the other hand, if Σ ab is nonsingular, its inverse can be obtained solving the next relation…”

Section: The Nc Approachmentioning

confidence: 99%

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

Abreu

Mendes

Oliveira

et al. 2012

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

In this work we carry out a noncommutative analysis of several Friedmann-Robert-Walker models, coupled to different types of perfect fluids and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. We notice that the noncommutative versions of these models show several relevant differences with respect to the correspondent commutative ones.

show abstract

“…However, in Ref. [39] this kind of problem was solved. On the other hand, if Σ ab is nonsingular, its inverse can be obtained solving the next relation…”

Section: The Nc Approachmentioning

confidence: 99%

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

Abreu

Mendes

Oliveira

et al. 2012

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is well known that systems which have vorticity and/or viscosity have Casimir invariants which obstruct the construction of a canonical formalism for a fluid, as demonstrated in [52]. However, this obstruction can be eliminated using the Clebsch parameters, as it was shown by Lin [53] and by two of us in [54]. In fact, with the introduction of Clebsch parameters, it is possible to obtain a Lagrangian density for the rotational fluid with dissipation, 3-dimensional, as being…”

Section: Hidden Symmetry In the Rotational Fluid Modelmentioning

confidence: 99%

Obtaining gauge invariant actions via symplectic embedding formalism

et al. 2012

Self Cite

View full text Add to dashboard Cite

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non-invariant ones. Both are named also as first- and second-class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non-invariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non-invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non-Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non-Abelian systems.Comment: 20 pages. Two-column format. Final version to appear in Annalen der Physik. arXiv admin note: substantial text overlap with arXiv:1001.2254, arXiv:hep-th/010908

show abstract

“…However, in Ref. [25] this kind of problem was solved. On the other hand, if Σ ab is nonsingular, its inverse can be obtained solving the relation below…”

Section: The Nc Generalized Symplectic Formalismmentioning

confidence: 99%

“…is the inverse of the symplectic matrix, this matrix can be computed by a straightforward calculation from the property r ) is given by f r, r = A( r, r ) C ( r, r ) −C( r, r ) B( r, r ) , (25) where A( r, r ), B( r, r ) and C ( r, r ) are arbitrary functions. From the properties above, the following general set of equations are obtained:…”

Section: Lagrangian Formulation Of the Noncommutative Irrotational Flmentioning

confidence: 99%

Lagrangian formulation of noncommutative fluid models

et al. 2010

Self Cite

View full text Add to dashboard Cite

In this work we study Lagrangian formulations for the noncommutative versions of the irrotational and rotational fluid models. These formulations will be obtained by using the Faddeev-Jackiw symplectic formalism. In this context, interesting results will be revealed, for example, a chiral behavior into both fluid models comes up. In fact, distinct and non-dynamically equivalent Lagrangian descriptions of the noncommutative versions of the fluid models can be proposed.

show abstract

Clebsch parameterization from the symplectic point of view

Cited by 19 publications

References 11 publications

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

Obtaining gauge invariant actions via symplectic embedding formalism

Lagrangian formulation of noncommutative fluid models

Contact Info

Product

Resources

About