Some comments on the universal constant in DSR

Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to avoid some fundamental problems (e.g. soccer ball problem), we argue that we should switch point of view and consider instead the Newton constant $G$ as the universal constant.Comment: 12 pages, Proceedings of DICE2006 (Piombino, Italy

And what if gravity is intrinsically quantic ?

Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum loop gravity are based on a quantum field theory - the latter is a quantum field theory of connections on a SU(2) group manifold and former a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics and gravity. Without gravity quantum mechanics becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum universe, and present a preliminary formulation for gravity in a system with a finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008 conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos remove

Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders

We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use reproduces the one proposed by Kempft, Mangano and Mann. It is emphasized that a minimal length acts as a natural regulator for the theory, thus eliminating the otherwise ever appearing infinities. So, we use our results to calculate the first correction to the Casimir Effect due to the minimal length. We also discuss some of the physical consequences of the existence of a minimal length, culminating in a proposal to reformulate the very concept of "position measurement"

Singular topologies in the Boulatov model

Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.Comment: 4 pages; proceedings of Loops'11 (May 2011, Madrid); v2: minor modifications matching published versio

Holonomic quantum computation in the presence of decoherence

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.Comment: I. F-G. Now publishes under name I. Fuentes-Schuller Published versio

From perceived autonomy support to intentional behaviour: Testing an integrated model in three healthy-eating behaviours

A motivational model integrating self-determination theory, the theory of planned behaviour, and the health action process approach was tested in three samples in three behavioural contexts: fruit and vegetable, breakfast, and snack consumption. Perceived support for autonomous (self-determined) forms of motivation from parents and autonomous motivation from self-determination theory were hypothesised to predict intention and behaviour indirectly via the mediation of attitude and perceived behavioural control from the theory of planned behaviour. It was also expected that planning strategies would mediate the effect of intention on behaviour. Relations in the proposed models were expected to be similar across the behaviours. A two-wave prospective design was adopted. Three samples of high-school students (total N = 1041; 59.60% female; M age = 17.13 years ± 1.57) completed measures of perceived autonomy support, autonomous motivation, theory of planned behaviour constructs, planning strategies and behaviour for each of the three behavioural contexts. Three months later, 816 participants (62,24% female; M age: 17.13 years, SD = 1.58) of the initial sample self-reported their behaviour referred to the previous three months. Structural equation models provided support for the key hypothesised effects of the proposed model for the three health-related behaviours. Two direct effects were significantly different across the three behaviours: the effect of perceived autonomy support on perceived behavioural control and the effect of attitude on intention. In addition, planning strategies mediated the effect of intention on behaviour in fruit and vegetable sample only. Findings extend knowledge of the processes by which psychological antecedents from the theories affect energy-balance related behaviours

Gravitational dynamics in Bose Einstein condensates

Analogue models for gravity intend to provide a framework where matter and gravity, as well as their intertwined dynamics, emerge from degrees of freedom that have a priori nothing to do with what we call gravity or matter. Bose Einstein condensates (BEC) are a natural example of analogue model since one can identify matter propagating on a (pseudo-Riemannian) metric with collective excitations above the condensate of atoms. However, until now, a description of the "analogue gravitational dynamics" for such model was missing. We show here that in a BEC system with massive quasi-particles, the gravitational dynamics can be encoded in a modified (semi-classical) Poisson equation. In particular, gravity is of extreme short range (characterized by the healing length) and the cosmological constant appears from the non-condensed fraction of atoms in the quasi-particle vacuum. While some of these features make the analogue gravitational dynamics of our BEC system quite different from standard Newtonian gravity, we nonetheless show that it can be used to draw some interesting lessons about "emergent gravity" scenarios.Comment: Replaced with published version. 15 pages, no figures, revtex4. Reference adde

Density fluctuations in κ\kappa-deformed inflationary universe

We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $\kappa-$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $\kappa-$deformation. We expand the non-local action in $H^2/\kappa^2$, with $H$ being the Hubble parameter and $\kappa$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/\kappa^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.Comment: final revision; 19 pages, 3 figures; to appear in Phys. Rev.

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited