Juan M. Romero

The Kepler Problem and Noncommutativity

We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of 10-58m2 gives observable corrections to the movement of the solar system. In this way, modifications in the physics of smaller scales imply modifications at large scales, something similar to the uv/ir mixing.

Newton's second law in a non-commutative space

In this Letter we show that corrections to Newtons second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force.

Snyder noncommutative space-time from two-time physics

We show that the two-time physics model leads to a mechanical system with Dirac brackets consistent with the Snyder noncommutative space. A Euclidean version of this space is also obtained and it is shown that both spaces have a dual system describing a particle in a curved space.

Note about the quantum of area in a noncommutative space

In this note we show that in a two-dimensional noncommutative space the area operator is quantized; this outcome is compared with the result obtained by loop quantum gravity methods.

Noncommutative spaces, the quantum of time, and Lorentz symmetry

We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are not commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.

The Area Quantum and Snyder Space

We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.

Alternative proposal to modified Newtonian dynamics

From a study of conserved quantities of the so-called Modified Newtonian Dynamics (MOND) we propose an alternative to this theory. We show that this proposal is consistent with the Tully-Fisher law, has conserved quantities whose Newtonian limit are the energy and angular momentum, and can be useful to explain cosmic acceleration. The dynamics obtained suggests that, when acceleration is very small, time depends on acceleration. This result is analogous to that of special relativity where time depends on velocity. PACS numbers: 95.35.+d, 45.20.Dd Nowadays there are various observational results in astrophysics whose explanation represents a challenge for theoretical physics. One of those problems is to explain the rotation curves of the galaxies. Observations indicate a relationship V 4 ∝ M for the speed V of the distant stars in a galaxy of mass M. However, as the only force acting on those stars is gravity and their trajectories are circles, Newtonian dynamics indicates that the relationship to hold is V 2 = GM/r, where r is the distance from the star to the center of the galaxy. To account for the difference, some authors assume the existence of a sort of matter that does not radiate: the so-called dark matter. There are, however, other proposals which assume modifications to the gravitational field or to the laws of dynamics. By considering the behavior of the speed of the distant stars, M. Milgrom proposed a modification to Newton’s second law as [1] m� (z) d 2 x i dt 2 = F

COSMOLOGICAL CONSTANT AND NONCOMMUTATIVITY: A NEWTONIAN POINT OF VIEW

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a Godel-type metric.

Very special relativity as particle in a gauge field and two-time physics

The action for a (3+1)-dimensional particle in very special relativity is studied. It is proved that massless particles only travel in effective (2 + 1)-dimensional space-time. It is remarkable that this action can be written as an action for a relativistic particle in a background gauge field and it is shown that this field causes the dimensional reduction. A new symmetry for this system is found. Furthermore, a general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contains very special relativity and two-time physics.

PRINCIPLE ACTION FOR PARTICLES FASTER THAN LIGHT

A general action for particles faster than light is presented. It is demonstrated that this action is invariant under reparametrizations. For several cases, it is shown that in the high velocity regime, the action is invariant under anisotropic spacetime transformation and at quantum level the system has fractal behavior. For those cases, it is shown that the action describes a particle in Finsler geometry and equivalent to one-dimensional field theory in a curved space, where the metric depends on temporal derivatives.