arXiv subjects

Osvaldo P. Santillán

Publications and source records attributed to Osvaldo P. Santillán.

7 recordsLinked to original sources

arXiv2026

Scattering amplitudes in Quadratic Graivty in a general formalism

In \cite{salvio}, inspired by the works \cite{pauli}-\cite{donogue}, a prescription for calculating the correlation functions in Quadratic Gravity \cite{stelle1}-\cite{stelle2} was presented and further exploited in \cite{salvio2}-\cite{salve}. A covariant formalism ensuring positive definite probabilities is worked out, which is the main drawback of Quadratic Gravity. The Gauss-Ostrogradsky method for Quadratic Gravity defines two momentum densities $P_1$ and $P_2$ and two coordinate densities $Q_1$ and $Q_2$, one pair is standard, the other ghost like. The approach in \cite{salvio} involves the continuation $P_2\to i P_2$ and $Q_2\to i Q_2$ of the ghost variables acting on kets $|>$ after taking mean values. The notable result is that, in the euclidean setting, this procedure leads to Quadratic Gravity path integral $Z(J)$, thus renormalizability is not spoiled. In view of these findings, it is natural to ask how the LSZ rules of the model have to be formulated, and this is the topic of the present work. A formalism adapted to full quartic or higher order theories is worked out, extending the results of \cite{yomismo}. The main technical point is to determine the creation annihilation algebra for the graviton modes, adapted to the present prescription, and properly dealing with gauge symmetry. This makes the problem harder than the quantization of the Pais-Uhlenbeck model. Two possible quantization schemes are discussed, they depend on whether the above prescriptions are applied at the beginning or at the end of the LSZ calculation.

hep-th↗

arXiv2024

Plateaux of probability for the expanded quantum infinite well

If the standard 1D quantum infinite potential well initially in its ground state suffers a sudden expansion, it turns out that in the evolution of the system they may appear plateaux of probability for some fractional times, as noticed by C. Aslangul in 2008. We introduce a mathematical framework to explain this phenomenon. Remarkably, the characterization of these plateaux depends on nontrivial number theoretical considerations.

quant-ph↗

arXiv2023

Exact quantum revivals for the Dirac equation

In the present work, the results obtained in [1] about the revivals of a relativistic fermion wave function on a torus are considerably enlarged. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the non relativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with non zero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed along the text.

quant-ph↗

arXiv2021

Some comments about emission channels of non abelian vortices

As is well established, several gauge theories admit vortices whose mean life time is very large. In some cases, this stability is a consequence of the topology of the symmetry group of the underlying theory. The main focus of the present work is, given a putative vortex, to determine if it is non abelian or not by analysis of its physical effects. The example considered here is the simplest one namely, a $SU(2)$ gauge model whose internal orientational space is described by $S^2$. Axion and gravitational emission are mainly considered. It is found that the non abelian property is basically reflected in a deviation of gravitational loop factor $γ_l$ found in \cite{vachaspati}-\cite{burden}. The axion emission instead, is not very sensitive to non abelianity, at least for this simple model. Another important discrepancy is that no point of the vortex reaches the speed of light when orientational modes are excited. In addition, the total power corresponding to each of these channels is compared, thus adapting the results of \cite{davis}-\cite{peloso} to the non abelian context. The excitations considered here are simple generalizations of rotating or spike string ansatz known in the literature \cite{ruso1}-\cite{kruczenski}. It is suggested however, that for certain type of semi-local strings whose internal moduli space is non compact, deviations due to non abelianity may be more pronounced.

hep-th↗

arXiv2017

Emergent Universe as an interaction in the dark sector

A cosmological scenario where dark matter interacts with a variable vacuum energy for a spatially flat Friedmann-Robertson-Walker space-time is proposed and analysed to show that with a linear equation of state and a particular interaction in the dark sector it is possible to get a model of an Emergent Universe. In addition, the viability of two particular models is studied by taking into account recent observations. The updated observational Hubble data and the JLA supernovae data are used in order to constraint the cosmological parameters of the models and estimate the amount of dark energy in the radiation era. It is shown that the two models fulfil the severe bounds of $Ω_{x}(z\simeq 1100)<0.009$ at the $2σ$ level of Planck.

gr-qc↗

arXiv2015

Power spectra in extended tachyon cosmologies

In the present work the power spectrum of a particular class of tachyon fields is compared with the one corresponding to a cosmological constant model. This is done for different barotropic indexes $γ_0$ and the background space time is assumed to be of the spatially flat Friedmann-Robertson-Walker type. The differential equation describing the perturbations is solved numerically and the power spectrum at the scale factor value $a=1$ is plotted for each case. The result is that the power spectrum of the standard tachyon field differs in many magnitude orders from the $Λ$CDM. However, the one with $γ_0=1.91$, which corresponds to a complementary tachyon field, coincides fairly well with the concordance model. Therefore, we conclude that the perturbed solutions constitute an effective method to distinguish between the different $γ_0$ values for the tachionization $Λ$CDM model and the fiducial model. The Statefinder parameters $\{r, s\}$, measuring the deviations of the analysed model from the concordance model, are also explicitly calculated. Our result suggest that, depending on the value of $γ_0$, these models can explain the observed expansion history or the perturbation power spectrum of the universe, but they may have problems in describing both features simultaneously.

gr-qc↗

arXiv2015

Double Higgs mechanisms, supermassive stable particles and the vacuum energy

In the present work it is shown that some specific double Higgs like mechanisms may have interesting cosmological applications. A hidden scenario which cast long lived super heavy particles together with an extremely light particle $a$ with mass $m_a\sim 10^{-32}-10^{-33}$eV is presented. The potential energy of this particle models the vacuum energy density of the universe $ρ_c\simeq 10^{-47}\;\hbox{GeV}^4$. The construction of such scenario is non trivial since the presence of light particles may spoil the stability of the heavy particles. However, double Higgs mechanisms may be helpful for overcoming this problem. The hidden sector we propose include fermions with masses near the neutrino mass $m_ν\sim 10^{-2}$eV which arise in terms of a see saw mechanism. Besides, the super heavy particles acquire a mass due to a double Higgs like mechanism of the order of the GUT scale. The gauge group of the model is $\hbox{SU(2)}_L$ and the scalars of the double Higgs mechanism are not charged under these interactions. The light particle $a$ is the Goldstone boson associated to a Peccei-Quinn like symmetry in the double Higgs model. In addition, the double Higgs mechanism posses another CP odd scalar $A^0$, which acquire a mass of the order of the GUT scale. We show that if there is no direct coupling between $A^0$ and $a$, even in presence of indirect couplings, the $A^0$ particle is long lived an may appear in events above the GKZ bound in present times.

hep-th↗