133 research outputs found
Oscillating universes as eigensolutions of cosmological Schr\"odinger equation
We propose a cosmological model which could explain, in a very natural way,
the apparently periodic structures of the universe, as revealed in a series of
recent observations. Our point of view is to reduce the cosmological
Friedman--Einstein dynamical system to a sort of Schr\"odinger equation whose
bound eigensolutions are oscillating functions. Taking into account the
cosmological expansion, the large scale periodic structure could be easily
recovered considering the amplitudes and the correlation lengths of the galaxy
clusters.Comment: 12 pages, Latex, submitted to Int. Jou. of Theor. Phy
Higher-Dimensional Twistor Transforms using Pure Spinors
Hughston has shown that projective pure spinors can be used to construct
massless solutions in higher dimensions, generalizing the four-dimensional
twistor transform of Penrose. In any even (Euclidean) dimension d=2n,
projective pure spinors parameterize the coset space SO(2n)/U(n), which is the
space of all complex structures on R^{2n}. For d=4 and d=6, these spaces are
CP^1 and CP^3, and the appropriate twistor transforms can easily be
constructed. In this paper, we show how to construct the twistor transform for
d>6 when the pure spinor satisfies nonlinear constraints, and present explicit
formulas for solutions of the massless field equations.Comment: 17 pages harvmac tex. Modified title, abstract, introduction and
references to acknowledge earlier papers by Hughston and other
k-deformed Poincare algebras and quantum Clifford-Hopf algebras
The Minkowski spacetime quantum Clifford algebra structure associated with
the conformal group and the Clifford-Hopf alternative k-deformed quantum
Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem
context. The resulting algebra is equivalent to the deformed anti-de Sitter
algebra U_q(so(3,2)), when the associated Clifford-Hopf algebra is taken into
account, together with the associated quantum Clifford algebra and a (not
braided) deformation of the periodicity Atiyah-Bott-Shapiro theorem.Comment: 10 pages, RevTeX, one Section and references added, improved content
Cartoon Computation: Quantum-like computing without quantum mechanics
We present a computational framework based on geometric structures. No
quantum mechanics is involved, and yet the algorithms perform tasks analogous
to quantum computation. Tensor products and entangled states are not needed --
they are replaced by sets of basic shapes. To test the formalism we solve in
geometric terms the Deutsch-Jozsa problem, historically the first example that
demonstrated the potential power of quantum computation. Each step of the
algorithm has a clear geometric interpetation and allows for a cartoon
representation.Comment: version accepted in J. Phys.A (Letter to the Editor
The general classical solution of the superparticle
The theory of vectors and spinors in 9+1 dimensional spacetime is introduced
in a completely octonionic formalism based on an octonionic representation of
the Clifford algebra \Cl(9,1). The general solution of the classical
equations of motion of the CBS superparticle is given to all orders of the
Grassmann hierarchy. A spinor and a vector are combined into a
Grassmann, octonionic, Jordan matrix in order to construct a superspace
variable to describe the superparticle. The combined Lorentz and supersymmetry
transformations of the fermionic and bosonic variables are expressed in terms
of Jordan products.Comment: 11 pages, REVTe
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
Test Matter in a Spacetime with Nonmetricity
Examples in which spacetime might become non-Riemannian appear above Planck
energies in string theory or, in the very early universe, in the inflationary
model. The simplest such geometry is metric-affine geometry, in which {\it
nonmetricity} appears as a field strength, side by side with curvature and
torsion. In matter, the shear and dilation currents couple to nonmetricity, and
they are its sources. After reviewing the equations of motion and the Noether
identities, we study two recent vacuum solutions of the metric-affine gauge
theory of gravity. We then use the values of the nonmetricity in these
solutions to study the motion of the appropriate test-matter. As a
Regge-trajectory like hadronic excitation band, the test matter is endowed with
shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late
Covariant Quantization of Superstrings Without Pure Spinor Constraints
We construct a covariant quantum superstring, extending Berkovits' approach
by introducing new ghosts to relax the pure spinor constraints. The central
charge of the underlying Kac-Moody algebra, which would lead to an anomaly in
the BRST charge, is treated as a new generator with a new b-c system. We
construct a nilpotent BRST current, an anomalous ghost current and an
anomaly-free energy-momentum tensor. For open superstrings, we find the correct
massless spectrum. In addition, we construct a Lorentz invariant B-field to be
used for the computation of the integrated vertex operators and amplitudes.Comment: 30 page
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