257 research outputs found
Higgs field as the gauge field corresponding to parity in the usual space-time
We find that the local character of field theory requires the parity degree
of freedom of the fields to be considered as an additional dicrete fifth
dimension which is an artifact emerging due to the local description of
space-time. Higgs field arises as the gauge field corresponding to this
discrete dimension. Hence the noncommutative geometric derivation of the
standard model follows as a manifestation of the local description of the usual
space-time.Comment: 14 pages, latex, no figure
Comments on the Entanglement Entropy on Fuzzy Spaces
We locate the relevant degrees of freedom for the entanglement entropy on
some 2+1 fuzzy models. It is found that the entropy is stored in the near
boundary degrees of freedom. We give a simple analytical derivation for the
area law using like expansion when only the near boundary degrees of
freedom are incorporated. Numerical and qualitative evidences for the validity
of near boundary approximation are finally given .Comment: 14 pages, 2 figure
Noncommutative scalar field minimally coupled to gravity
A model for noncommutative scalar fields coupled to gravity based on the
generalization of the Moyal product is proposed. Solutions compatible with
homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial
order in the perturbation of the star-product are presented. It is shown that
in the context of a typical chaotic inflationary scenario, at least in the
slow-roll regime, noncommutativity yields no observable effect.Comment: Talk presented at the Workshop on Quantum Gravity and Noncommutative
Geometry, 20-23 July 2004, Universidade Lus\'ofona, Lisbon, Portugal. To
appear at Int. J. Mod. Phys.
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
A detailed description of the infinite-dimensional Lie algebra of star-gauge
transformations in noncommutative Yang-Mills theory is presented. Various
descriptions of this algebra are given in terms of inner automorphisms of the
underlying deformed algebra of functions on spacetime, of deformed symplectic
diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of
compact operators on a quantum mechanical Hilbert space. The spacetime and
string interpretations are also elucidated.Comment: 49 pages LaTeX; v2: References added; v3: Typos corrected and
references added; final version published in JHE
Spacetime Noncommutativity and Antisymmetric Tensor Dynamics in the Early Universe
This paper investigates the possible cosmological implications of the
presence of an antisymmetric tensor field related to a lack of commutatitivity
of spacetime coordinates at the Planck era. For this purpose, such a field is
promoted to a dynamical variable, inspired by tensor formalism. By working to
quadratic order in the antisymmetric tensor, we study the field equations in a
Bianchi I universe in two models: an antisymmetric tensor plus scalar field
coupled to gravity, or a cosmological constant and a free massless
antisymmetric tensor. In the first scenario, numerical integration shows that,
in the very early universe, the effects of the antisymmetric tensor can prevail
on the scalar field, while at late times the former approaches zero and the
latter drives the isotropization of the universe. In the second model, an
approximate solution is obtained of a nonlinear ordinary differential equation
which shows how the mean Hubble parameter and the difference between
longitudinal and orthogonal Hubble parameter evolve in the early universe.Comment: 25 pages, Revtex file, 4 figures in attachmen
Is there an imprint of Planck scale physics on inflationary cosmology?
We study the effects of the trans-Planckian dispersion relation on the
spectrum of the primordial density perturbations during inflation. In contrast
to the earlier analyses, we do not assume any specific form of the dispersion
relation and allow the initial state of the field to be arbitrary. We obtain
the spectrum of vacuum fluctuations of the quantum field by considering a
scalar field satisfying the linear wave equation with higher spatial derivative
terms propagating in the de Sitter space-time. We show that the power spectrum
does not strongly depend on the dispersion relation and that the form of the
dispersion relation does not play a significant role in obtaining the
corrections to the scale invariant spectrum. We also show that the signatures
of the deviations from the flat scale-invariant spectrum from the CMBR
observations due to quantum gravitational effects cannot be differentiated from
the standard inflationary scenario with an arbitrary initial state.Comment: 6 pages, uses RevTex4; References added; Final versio
About maximally localized states in quantum mechanics
We analyze the emergence of a minimal length for a large class of generalized
commutation relations, preserving commutation of the position operators and
translation invariance as well as rotation invariance (in dimension higher than
one). We show that the construction of the maximally localized states based on
squeezed states generally fails. Rather, one must resort to a constrained
variational principle.Comment: accepted for publication in PR
Angles in Fuzzy Disc and Angular Noncommutative Solitons
The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region
in a noncommutative plane, and is a fuzzy approximation of a commutative disc.
In this paper we show that one can introduce a concept of angles to the fuzzy
disc, by using the phase operator and phase states known in quantum optics. We
gave a description of a fuzzy disc in terms of operators and their commutation
relations, and studied properties of angular projection operators. A similar
construction for a fuzzy annulus is also given. As an application, we
constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy
disc, which corresponds to a fan-shaped D-brane. We also applied this concept
to the theory of noncommutative gravity that we proposed in Ref.[2]. In
addition, possible connections to black hole microstates, holography and an
experimental test of noncommutativity by laser physics are suggested.Comment: 24 pages, 12 figures; v2: minor mistake corrected in Eq.(3.21), and
discussion adapted accordingly; v3: a further discussion on the algebra of
the fuzzy disc added in subsection 3.2; v4: discussions improved and typos
correcte
Bosonic Description of Spinning Strings in Dimensions
We write down a general action principle for spinning strings in 2+1
dimensional space-time without introducing Grassmann variables. The action is
written solely in terms of coordinates taking values in the 2+1 Poincare group,
and it has the usual string symmetries, i.e. it is invariant under a)
diffeomorphisms of the world sheet and b) Poincare transformations. The system
can be generalized to an arbitrary number of space-time dimensions, and also to
spinning membranes and p-branes.Comment: Latex, 12 page
Noncommutative field gas driven inflation
We investigate early time inflationary scenarios in an Universe filled with a
dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic
gas is a gas composed of bosonic scalar field with noncommutative field space
on a commutative spacetime. Such noncommutative field theories was recently
introduced as a generalization of quantum mechanics on a noncommutative
spacetime. As key features of these theories are Lorentz invariance violation
and CPT violation. In the present study we use a noncommutative bosonic field
theory that besides the noncommutative parameter shows up a further
parameter . This parameter controls the range of the
noncommutativity and acts as a regulator for the theory. Both parameters play a
key role in the modified dispersion relations of the noncommutative bosonic
field, leading to possible striking consequences for phenomenology. In this
work we obtain an equation of state for the
noncommutative bosonic gas relating pressure and energy density , in
the limit of high temperature. We analyse possible behaviours for this gas
parameters , and , so that , which
is the region where the Universe enters an accelerated phase.Comment: Reference added. Version to appear in Journal of Cosmology and
Astroparticle Physics - JCA
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