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F. Rodenas

Publications and source records attributed to F. Rodenas.

9 recordsLinked to original sources
arXiv2016

The Specification Property for $C_0$-Semigroups

We study one of the strongest versions of chaos for continuous dynamical systems, namely the specification property. We extend the definition of specification property for operators on a Banach space to strongly continuous one-parameter semigroups of operators, that is, $C_0$-semigroups. In addition, we study the relationships of the specification property for $C_0$-semigroups (SgSP) with other dynamical properties: mixing, Devaney's chaos, distributional chaos and frequent hypercyclicity. Concerning the applications, we provide several examples of semigroups which exhibit the SgSP with particular interest on solution semigroups to certain linear PDEs, which range from the hyperbolic heat equation to the Black-Scholes equation.

math.FA↗
arXiv1997

Twisted h-spacetimes and invariant equations

We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the representations of one of the deformed spacetime algebras, we discuss the Klein-Gordon operator. It is found that the h-deformed d'Alembertian has plane wave solutions of the same form as the standard ones. We also give explicit expressions for the h-gamma matrices defining the associated Dirac equations.

q-alg↗
arXiv1995

Deformed Minkowski spaces: clasification and properties

Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups, which reproduces a previous classification by Woronowicz and Zakrzewski. As a consequence of the unified analysis presented, we give the commutation properties, the deformed (and central) length element and the metric tensor for the different spacetime algebras.

q-alg↗
arXiv1995

On the physical contents of q-deformed Minkowski spaces

Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.

hep-th↗
arXiv1994

Differential calculus on q-Minkowski space

We wish to report here on a recent approach to the non-commutative calculus on $q$-Minkowski space which is based on the reflection equations with no spectral parameter. These are considered as the expression of the invariance (under the coaction of the $q$-Lorentz group) of the commutation properties which define the different $q$-Minkowski algebras. This approach also allows us to discuss the possible ambiguities in the definition of $q$-Minkowski space ${\cal M}_q$ and its differential calculus. The commutation relations among the generators of ${\cal M}_q$ (coordinates), ${\cal D}_q$ (derivatives), $Λ_q$ (one-forms) and a few invariant (scalar) operators are established and compared with earlier results.

hep-th↗
arXiv1994

Quantum groups and deformed special relativity

The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its covariance properties as described by appropriate reflection equations. Some isomorphisms among the space-time and derivative algebras are demonstrated, and their representations are described briefly. Finally, some physical consequences and open problems are discussed.

hep-th↗