Noncommutative cosmologies

Burić, Maja; Grammatikopoulos, Theodoros; Madore, J.; Zoupanos, George

doi:10.1088/1742-6596/53/1/053

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…In particular, some representative noncommutative field theories which are formulated employing the star‐product and the Seiberg‐Witten map [ 22 ] (see also [23]) can be found in refs [24–36], while some indicative publications in which the matrix treatment of noncommutativity (matrix geometries) is adopted leading to matrix models can be found in refs [37–41]. For an alternative approach see also refs [42–44], in which it is described that the degrees of freedom of the resulting gravitational theory are associated to those of the noncommutative structure. Last, a very recent and systematic approach on constructing noncommutative field theories using braided

L_{\infty}

‐algebras can be found in refs [45, 46].…”

Section: Introductionmentioning

confidence: 99%

Four‐Dimensional Gravity on a Covariant Noncommutative Space (II)

Manolakos

Manousselis

Zoupanos

2021

Fortschritte der Physik

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Based on the construction of the 4‐dim noncommutative gravity model described in our previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4‐dim de Sitter space), which accommodates the gravity model, is presented and then the corresponding field equations, which are obtained after variation of the previously proposed action, are extracted. Also, a spontaneous breaking of the initial symmetry is performed, this time induced by the introduction of an auxiliary scalar field, and its implications in the reduced theory, which is produced after considering the commutative limit, are examined.

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L_{\infty}

‐algebras can be found in refs [45, 46].…”

Section: Introductionmentioning

confidence: 99%

Four‐Dimensional Gravity on a Covariant Noncommutative Space (II)

Manolakos

Manousselis

Zoupanos

2021

Fortschritte der Physik

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“…There has been great interest in the study of physical theories on noncommutative spaces. The motivation is partly the natural appearance of noncommutative spaces in some areas of physics, for example in the string theory ( [1][2][3][4][5], for example). In particular, it has been understood that the canonical relation…”

Section: Introductionmentioning

confidence: 99%

Closedness of orbits in a space with SU(2) Poisson structure

Fatollahi

Shariati

Khorrami

2014

Int. J. Mod. Phys. A

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The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all of the bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of the motion is also worked out.

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“…Over the passed few years a noncommutative generalization of the Cartan frame formalism has been developed [2,3] and applied [4][5][6][7] with varying degrees of success to problems in gravitational physics, notably to the possibility of blowing up [8] the Big Bang. One distinguishing feature of this formalism is that the field equations are not derived from an action principle but rather from constraints imposed on the frame arising from Jacobi identities.…”

Section: Introductionmentioning

confidence: 99%