arXiv subjects

José David Vergara

Publications and source records attributed to José David Vergara.

4 recordsLinked to original sources

arXiv2019

Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type

A general formula is calculated for the connection of a central metric w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using the framework of linear connections on central bi-modules. The general formula is further on used to calculate the corresponding Riemann tensor and prove the corresponding Bianchi identities and certain symmetries that are essential to obtain a symmetric and divergenceless Einstein Tensor. In particular, the obtained Einstein Tensor is not equivalent to the sum of the noncommutative Riemann tensor and scalar, as in the commutative case, but in addition a traceless term appears.

math-ph↗

arXiv2017

A Poincaré Covariant Noncommutative Spacetime?

We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative spacetime with a minimal length that is given by the mass. By using this operator to define a noncommutative spacetime, we obtain a Poincaré invariant noncommutative spacetime and in addition solve the soccer-ball problem. Moreover, from recent progress in deformation theory we extract the idea how to obtain, in a physical and mathematical well-defined manner, an emerging noncommutative spacetime. This is done by a strict deformation quantization known as Rieffel deformation (or warped convolutions). The result is a noncommutative spacetime combining a Snyder and a Moyal-Weyl type of noncommutativity that in addition behaves covariant under transformations of the \textbf{whole} Poincaré group.

math-ph↗

arXiv2013

Higher Order Theories and its Relationship with Noncommutativity

We present a relationship between noncommutativity and higher order time derivative theories using a method perturbative. We introduce a generalization of the Chern-Simons Quantum Mechanics for higher order time derivatives. This model presents noncommutativity in a natural way when we project to states of low energy. Compared with the usual model, our system presents noncommutativity without the necessity of taking the limit of strong field. We quantized the theory using a Bopp's shift of the noncommutative variables and we obtain an spectrum without negatives energies. In addition we extend the model to high order derivatives and noncommutativity with variable dependent parameter.

hep-th↗

arXiv2011

Lorentz violation, Two times physics and Strings

We study a recently proposed generalization of the relativistic particle by Kostelecký, that includes explicit Lorentz violation. We present an alternative action for this system and we show that this action can be interpreted as a particle in curved space with a metric that depends on the Lagrange multipliers. Furthermore, the following results are established for this model: (i) there exists a limit where this system has more local symmetries that the usual relativistic particle; (ii) in this limit if we restore the Lorentz symmetry we obtain a direct relationship with the two time physics; (iii) also we show that if we intent to restore the Poincaré symmetry we obtain the action of the relativistic bosonic string.

hep-th↗