15 research outputs found
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.Comment: 11 pages latex, misprints corrected, version to appear in PR
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.Comment: 15 pages revtex. The title has been modified,the paper shortened and
misprints have been corrected. Version to appear in JHE
Maximally localized states and causality in non commutative quantum theories
We give simple representations for quantum theories in which the position
commutators are non vanishing constants. A particular representation reproduces
results found using the Moyal star product. The notion of exact localization
being meaningless in these theories, we adapt the notion of ``maximally
localized states'' developed in another context . We find that gaussian
functions play this role in a 2+1 dimensional model in which the non
commutation relations concern positions only. An interpretation of the wave
function in this non commutative geometry is suggested. We also analyze higher
dimensional cases. A possible incidence on the causality issue for a Q.F.T with
a non commuting time is sketched.Comment: 11 pages, Revtex. The presentation has been improved, the subsection
on high dimensions has been modified. This version will appear in PR
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.Comment: 9 pages revtex, 4 figures,version to appear in PR
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 limit, they reproduce some properties of the ordinary coherent states
on the non commutative plane.Comment: 18 pages, Latex. Minor changes in notations. Version to appear in
JHE
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.Comment: 19 Pages, Revtex4; V2 Final version, To appear in Phys. Rev. D., 1
figure and references adde
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.Comment: 10 pages revtex, 1 figur