arXiv subjects

Musongela Lubo

Publications and source records attributed to Musongela Lubo.

13 recordsLinked to original sources

arXiv2025

Factorization, Supersymmetry, Coherent States and Classical Trajectories

A generalization of coherent states has been developed in the context of supersymmetric quantum mechanics. For many cases, no link has been made with the corresponding classical system. In this work, we consider simple superpotentials and compare the classical trajectories and the mean values of the position operator in these states. The mean value of the position operator can be written as a power series in time with coefficients whose relations to the superpotential are given in the general case. These coefficients imply integrals and recursion formulas. The method used reproduces exactly what is known for the harmonic oscillator. It is extended to study a family of systems which encompasses the harmonic oscillator. We also consider a third degree superpotential. The time scale after which the mean value of the position operator and the classical trajectory begin differing significantly is evaluated. Keywords: Coherent States, SUSYQM.

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arXiv2023

The Higgs Boson and The Fakeon Hypothesis

In this paper, we make an attempt to implement the fakeon hypothesis in particle physics. To begin with, we consider a model in which the Higgs boson is the only fakeon. We deduce its interactions with the electroweak gauge bosons. Each such new interaction can be written as a product of two factors. The first one depends, on the electroweak gauge bosons and their derivatives. The second one solely depends, on the physical Higgs and its derivatives. We also study the conserved quantities of different (free) fields in this setting.

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arXiv2008

Can Born Infeld Gravity Explain Galaxy Rotation Curves?

A Born-Infeld theory has been proposed in order to explain both dark matter and dark energy. We show that the approximation used to deduce the flat rotation curves in this model breaks down at large distances in a spherically symmetric configuration.

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arXiv2005

Gauge-invariant perturbation theory for trans-Planckian inflation

The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics -- dubbed as trans-Planckian inflation -- has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyzes, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner -- without calculating the stress-tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gauge-invariant cosmological perturbations for the single-scalar field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit time-like vector field which defines a preferred rest frame. We show that: (i) The non-linear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different than those presumed in the earlier analyzes. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power-spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.

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arXiv2005

The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States

A family of states built from the uncertainty principle on the fuzzy sphere has been shown to reproduce the stereographic projection in the large $j$ limit. These generalized squeezed states are used to construct an associative star product which involves a finite number of derivatives on its primary functional space. It is written in terms of a variable on the complex plane. We show that it actually coincides with the one found by H.Gross and P.Presnajder in the simplest cases, endowing the later with a supplementary physical interpretation. We also show how the spherical harmonics emerge in this setting.

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arXiv2005

A Brane model with two asymptotic regions

Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip.S.Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.

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arXiv2005

Global Defects In Theories With Lorentz Symmetry Violation

We study global topological defects in the Jacobson-Corley model which breaks Lorentz symmetry and involves up to fourth order derivatives. There is a window in the parameter space in which no solution exists. Otherwise, different profiles are allowed for the same values of the parameters. For a scale of Lorentz violation much higher than the scale of gauge symmetry breaking, the energy densities are higher, of the same order or smaller than in the usual case for domain walls, cosmic strings and hedgehogs respectively. Possible cosmological implications are suggested.

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arXiv2004

Quantum mechanics on non commutative spaces and squeezed states: a functional approach

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and the commutators in these theories generically leads to a harmonic oscillator whose positions and momenta mean values are not strictly equal to the ones predicted by classical mechanics. This raises the question of the nature of quasi classical states in these models. We propose an extension based on a variational principle. The action considered is the sum of the absolute values of the expressions associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory i.e we recover the known Gaussian functions. Besides them, we find other states which can be expressed as products of Gaussians with specific hyper geometrics. We illustrate our construction in two models defined on a four dimensional phase space: a model endowed with a minimal length uncertainty and the non commutative plane. Our proposal leads to second order partial differential equations. We find analytical solutions in specific cases. We briefly discuss how our proposal may be applied to the fuzzy sphere and analyze its shortcomings.

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arXiv2004

The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection

On the fuzzy sphere, no state saturates simultaneously all the Heisenberg uncertainties. We propose a weaker uncertainty for which this holds. The family of states so obtained is physically motivated because it encodes information about positions in this fuzzy context. In particular, these states realize in a natural way a deformation of the stereographic projection. Surprisingly, in the large $j$ limit, they reproduce some properties of the ordinary coherent states on the non commutative plane.

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arXiv2003

Ultraviolet cut off and Bosonic Dominance

We rederive the thermodynamical properties of a non interacting gas in the presence of a minimal uncertainty in length. Apart from the phase space measure which is modified due to a change of the Heisenberg uncertainty relations, the presence of an ultraviolet cut-off plays a tremendous role. The theory admits an intrinsic temperature above which the fermion contribution to energy density, pressure and entropy is negligible.

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arXiv2003

Ultraviolet cut off, black hole-radiation equilibrium and big bang

In the presence of a minimal uncertainty in length, there exists a critical temperature above which the thermodynamics of a gas of radiation changes drastically. We find that the equilibrium temperature of a system composed of a Schwarzschild black hole surrounded by radiation is unaffected by these modifications. This is in agreement with works related to the robustness of the Hawking evaporation. The only change the deformation introduces concerns the critical volume at which the system ceases to be stable. On the contrary, the evolution of the very early universe is sensitive to the new behavior. We readdress the shortcomings of the standard big bang model(flatness, entropy and horizon problems) in this context, assuming a minimal coupling to general relativity. Although they are not solved, some qualitative differences set in.

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arXiv2001

The stress-energy tensor for trans-Planckian cosmology

This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian modes in black hole physics and in cosmology. This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their backreaction during inflation. It is shown that gravitational waves of trans-Planckian momenta but subhorizon frequencies cannot account for the form of cosmic vacuum energy density observed at present, contrary to a recent claim. The backreaction effects during inflation are confirmed to be important and generic for those dispersion relations that are liable to induce changes in the power spectrum of metric fluctuations. Finally, it is shown that in pure de Sitter inflation there is no modification of the power spectrum except for a possible magnification of its overall amplitude independently of the dispersion relation.

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arXiv1999

Quantum Minimal Length and Transplanckian Photons

In this paper we first give arguments supporting the idea that a B.T.Z black hole can face a transplankian problem even when its mass is small. K.M.M quantum theory is applied to the Hawking evaporation of the Schwarzchild and B.T.Z black holes. Working in the physically safe quasi position representation, we argue that the oscillating term present in a previous analysis is removed so that actually one doesn't need an average procedure. We expand the s wave function as the exponential of a series in the minimal length of the new quantum theory. This reduces an infinite order differential equation to a numerable set of finite order ones. We obtain the striking result that the infinity of arbitrary constants induced by the order of the wave equation has no physical meaning due to normalization. We finally construct gaussian wave pacqets and study their trajectories. We suggest a quantitative description of the non locality zone and its dependance on the K.M.M energy scale. Potential incidences on unitarity are briefly evoqued.

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