4,842 research outputs found
Hybrid quantization of an inflationary model: The flat case
We present a complete quantization of an approximately homogeneous and
isotropic universe with small scalar perturbations. We consider the case in
which the matter content is a minimally coupled scalar field and the spatial
sections are flat and compact, with the topology of a three-torus. The
quantization is carried out along the lines that were put forward by the
authors in a previous work for spherical topology. The action of the system is
truncated at second order in perturbations. The local gauge freedom is fixed at
the classical level, although different gauges are discussed and shown to lead
to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant
quantities are considered. The reduced system is proven to admit a symplectic
structure, and its dynamical evolution is dictated by a Hamiltonian constraint.
Then, the background geometry is polymerically quantized, while a Fock
representation is adopted for the inhomogeneities. The latter is selected by
uniqueness criteria adapted from quantum field theory in curved spacetimes,
which determine a specific scaling of the perturbations. In our hybrid
quantization, we promote the Hamiltonian constraint to an operator on the
kinematical Hilbert space. If the zero mode of the scalar field is interpreted
as a relational time, a suitable ansatz for the dependence of the physical
states on the polymeric degrees of freedom leads to a quantum wave equation for
the evolution of the perturbations. Alternatively, the solutions to the quantum
constraint can be characterized by their initial data on the minimum-volume
section of each superselection sector. The physical implications of this model
will be addressed in a future work, in order to check whether they are
compatible with observations.Comment: 20 pages, no figures. v2: minor changes, in particular, abstract
shortened, final discussion improve
Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology
We study the evolution of a homogeneous and isotropic spacetime whose spatial
sections have three-torus topology, coupled to a massless scalar field with
small scalar perturbations within loop quantum cosmology. We consider a
proposal for the effective dynamics based on a previous hybrid quantization
completed by us. Consequently, we introduce a convenient gauge fixing and adopt
reduced canonical variables adapted to that hybrid quantum description.
Besides, we keep backreaction contributions on the background coming from terms
quadratic in the perturbations in the action of the system. We carry out a
numerical analysis assuming that the inhomogeneities were in a massless vacuum
state at distant past (where the initial data are set). At distant future, we
observe a statistical amplification of the modes amplitude in the infrared
region, as well as a phase synchronization arising from quantum gravity
phenomena. A description of the perturbations in terms of the Mukhanov-Sasaki
gauge invariants provides the same qualitative results. Finally, we analyze
some consequences of the backreaction in our effective description.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.
A complete hybrid quantization in inhomogeneous cosmology
A complete quantization of a homogeneous and isotropic spacetime with closed
spatial sections coupled to a massive scalar field is provided, within the
framework of Loop Quantum Cosmology. We identify solutions with their initial
data on the minimum volume section, and from this we construct the physical
Hilbert space. Moreover, a perturbative study allows us to introduce small
inhomogeneities. After gauge fixing, the inhomogeneous part of the system is
reduced to a linear field theory. We then adopt a standard Fock representation
to quantize these degrees of freedom. For the considered case of compact
spatial topology, the requirements of: i) invariance under the spatial
isometries, and ii) unitary implementation of the quantum dynamics, pick up a
unique Fock representation and a particular set of canonical fields (up to
unitary equivalence).Comment: 6 page
A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass
A major problem in the quantization of fields in curved spacetimes is the
ambiguity in the choice of a Fock representation for the canonical commutation
relations. There exists an infinite number of choices leading to different
physical predictions. In stationary scenarios, a common strategy is to select a
vacuum (or a family of unitarily equivalent vacua) by requiring invariance
under the spacetime symmetries. When stationarity is lost, a natural
generalization consists in replacing time invariance by unitarity in the
evolution. We prove that, when the spatial sections are compact, the criterion
of a unitary dynamics, together with the invariance under the spatial
isometries, suffices to select a unique family of Fock quantizations for a
scalar field with time dependent mass.Comment: 11 pages, version accepted for publication in Classical and Quantum
Gravit
Content Development for Leadership (SLO 23)
As the construction industry evolves, the curriculum that prepares future builders must change and account for new ideas and concepts as well. In September of 2020, the Construction Management department at the California Polytechnic State University (Cal Poly) gave the opportunity to five senior level students to assist them with research on how to develop content and programming for the five extra student learning outcomes and have it count toward their senior project. These five students, each being paired up with a student from CM 461, were asked to produce a study guide and survey questions for one of the five student learning outcomes. The purpose of this paper is to give a more in depth understanding of the logistics and process behind the whole senior project for the leadership student learning outcome. The study guide was inspired by a detailed literature review, collaboration and opinions of other students, and a reflection of students’ own professional experiences. The study guide covers leadership ideals and skills that a leader should have in order to be successful in the construction industry. The goal is to equip students with the tools that assure they will be great leaders and succeed in the construction industry
Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes
For Klein-Gordon fields, it is well known that there exist an infinite number
of nonequivalent Fock representations of the canonical commutation relations
and, therefore, of inequivalent quantum theories. A context in which this kind
of ambiguities arises and prevents the derivation of robust results is, e.g.,
in the quantum analysis of cosmological perturbations. In these situations,
typically, a suitable scaling of the field by a time dependent function leads
to a description in an auxiliary static background, though the nonstationarity
still shows up in a time dependent mass. For such a field description, and
assuming the compactness of the spatial sections, we recently proved in three
or less spatial dimensions that the criteria of a natural implementation of the
spatial symmetries and of a unitary time evolution are able to select a unique
class of unitarily equivalent vacua, and hence of Fock representations. In this
work, we succeed to extend our uniqueness result to the consideration of all
possible field descriptions that can be reached by a time dependent canonical
transformation which, in particular, involves a scaling of the field by a
function of time. This kind of canonical transformations modify the dynamics of
the system and introduce a further ambiguity in its quantum description,
exceeding the choice of a Fock representation. Remarkably, for any compact
spatial manifold in less than four dimensions, we show that our criteria
eliminate any possible nontrivial scaling of the field other than that leading
to the description in an auxiliary static background. Besides, we show that
either no time dependent redefinition of the field momentum is allowed or, if
this may happen, the redefinition does not introduce any Fock representation
that cannot be obtained by a unitary transformation.Comment: 37 pages. Modified title. Improved discussion concerning the spatial
symmetry group. New section (section VI
Ca II triplet spectroscopy of small magellanic cloud red giants. II. abundances for a sample of field stars
We have obtained metallicities of ∼360 red giant stars distributed in 15 Small Magellanic Cloud (SMC) fields from near-infrared spectra covering the Ca II triplet lines using the VLT + FORS2. The errors of the derived [Fe/H] values range from 0.09 to 0.35 dex per star, with a mean of 0.17 dex. The metallicity distribution (MD) of the whole sample shows a mean value of [Fe/H] = -1.00 ± 0.02, with a dispersion of 0.32 0.01, in agreement with global mean [Fe/H] values found in previous studies. We find no evidence of a metallicity gradient in the SMC. In fact, on analyzing the MD of each field, we derived mean values of [Fe/H] = -0.99 ± 0.08 and [Fe/H] = -1.02 ± 0.07 for fields located closer and farther than 4° from the center of the galaxy, respectively. In addition, there is a clear tendency for the field stars to be more metal-poor than the corresponding cluster they surround, independent of their positions in the galaxy and of the clusters' age. We argue that this most likely stems from the field stars being somewhat older and therefore somewhat more metal-poor than most of our clusters. © 2010. The American Astronomical Society.Fil: Parisi, Maria Celeste. Universidad Nacional de Cordoba. Observatorio Astronomico de Cordoba; ArgentinaFil: Geisler, Doug. Universidad de Concepción; ChileFil: Grocholski, A. J.. University of Florida; Estados Unidos. Space Telescope Science Institute; Estados UnidosFil: Claria Olmedo, Juan Jose. Universidad Nacional de Cordoba. Observatorio Astronomico de Cordoba; ArgentinaFil: Sarajedini, A.. University of Florida; Estados Unido
Prescriptions in Loop Quantum Cosmology: A comparative analysis
Various prescriptions proposed in the literature to attain the polymeric
quantization of a homogeneous and isotropic flat spacetime coupled to a
massless scalar field are carefully analyzed in order to discuss their
differences. A detailed numerical analysis confirms that, for states which are
not deep in the quantum realm, the expectation values and dispersions of some
natural observables of interest in cosmology are qualitatively the same for all
the considered prescriptions. On the contrary, the amplitude of the wave
functions of those states differs considerably at the bounce epoch for these
prescriptions. This difference cannot be absorbed by a change of
representation. Finally, the prescriptions with simpler superselection sectors
are clearly more efficient from the numerical point of view.Comment: 18 pages, 6 figures, RevTex4-1 + BibTe
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