Quantum mechanics in de Sitter space

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.Comment: 7 pages, LaTeX. Version published on Int. J. Theor. Phy

UV/IR Mixing in Nonassociative Snyder phi^4 Theory

Using a quantization of the nonassociative and noncommutative Snyder phi^4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D-, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter beta. We prove that these integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative phi^4 products can generate different momentum-conserving integrals. Finally most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore infrared divergences should exist, in general, in the Snyder phi^4 theory. We consider infrared divergences at the limit p -> 0 as UV-IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative phi^4 products. We also discuss the extrapolation of the Snyder deformation parameter beta to negative values as well as certain general properties of one-loop quantum corrections in Snyder phi^4 theory at the zero-momentum limit.Comment: 14 pages, 3 figures, version to be published in Phys. Rev.

Nonassociative Snyder phi4 Quantum Field Theory

In this article we define and quantize a truncated form of the nonassociative and noncommutative Snyder phi^4 field theory using the functional method in momentum space. More precisely, the action is approximated by expanding up to the linear order in the Snyder deformation parameter beta, producing an effective model on commutative spacetime for the computation of the two-, four- and six-point functions. The two- and four-point functions at one loop have the same structure as at the tree level, with UV divergences faster than in the commutative theory. The same behavior appears in the six-point function, with a logarithmic UV divergence and renders the theory unrenormalizable at beta^1 order except for the special choice of free parameters s_1=-s_2. We expect effects from nonassociativity on the correlation functions at beta^1 order, but these are cancelled due to the average over permutations.Comment: 13 pages, 6 figures. Version to be published in Phys.Rev.

Symmetry Breaking, Central Charges and the AdS_2/CFT_1 Correspondence

When two-dimensional Anti-de Sitter space (AdS_2) is endowed with a non-constant dilaton the origin of the central charge in the Virasoro algebra generating the asymptotic symmetries of AdS_2 can be traced back to the breaking of the SL(2,R) isometry group of AdS_2. We use this fact to clarify some controversial results appeared in the literature about the value of the central charge in these models.Comment: version 3, some points have been clarifie

Relative-locality phenomenology on Snyder spacetime

We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $\kappa$-Poincar\'e models: for example, in the Snyder case the action of the Lorentz group is preserved, and the composition law of momenta is deformed by terms quadratic in the inverse Planck energy. From the investigation of time delay and dual curvature lensing we deduce that, because of these differences, in the Snyder case the properties of the detector are essential for the observation of relative locality effects. The deviations from special relativity do not depend on the energy of the particles and are much smaller than in the $\kappa$-Poincar\'e case, so that are beyond the reach of present astrophysical experiments. However, these results have a conceptual interest, because they show that relative-locality effects can occur even if the action of the Lorentz group on phase space is not deformed

Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

We investigate static, planar, solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for hairy black brane solutions with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall solution at $r=\infty$ and an AdS solution near $r=0$.Comment: 5 pages, no figure

Twist for Snyder space

We construct the twist operator for the Snyder space. Our starting point is a non-associative star product related to a Hermitian realisation of the noncommutative coordinates originally introduced by Snyder. The corresponding coproduct of momenta is non-coassociative. The twist is constructed using a general definition of the star product in terms of a bi-differential operator in the Hopf algebroid approach. The result is given by a closed analytical expression. We prove that this twist reproduces the correct coproducts of the momenta and the Lorentz generators. The twisted Poincar\'{e} symmetry is described by a non-associative Hopf algebra, while the twisted Lorentz symmetry is described by the undeformed Hopf algebra. This new twist might be important in the construction of different types of field theories on Snyder space.Comment: 15 pages, references added, matches published versio

Casimir effect in Snyder space

We show that two indistinguishable aspects of the divergences occurring in the Casimir effect, namely the divergence of the energy of the higher modes and the non-compactness of the momentum space, get disentangled in a given noncommutative setup. To this end, we consider a scalar field between two parallel plates in an anti-Snyder space. Additionally, the large mass decay in this noncommutative setup is not necessarily exponential.Facultad de Ciencias Exacta