515 research outputs found
On the SU(3) parametrization of qutrits
Parametrization of qutrits on the complex projective plane CP^2 = SU(3)/U(2)
is given explicitly. A set of constraints that characterize mixed state density
matrices is found.Comment: Paper presented at 12th Central European Workshop on Quantum Optics,
6-9 June 2005, Bilkent Univ., Ankara, Turke
An Exact Cosmological Solution of the Coupled Einstein-Majorana Fermion-Scalar Field Equations
We couple a neutral scalar field and a Majorana fermion field to Einstein
gravity represented by the Robertson-Walker metric and find a class of exact
cosmological solutions
Electroweak Theory and Noncommutative Geometry
The noncommutative generalisation of the standard electroweak model due to
Balakrishna, Gursey and Wali is formulated in terms of the derivations
Der_2(M_3) of a three dimensional representation of the su(2) Lie algebra of
weak isospin. A light Higgs boson of mass about 130 GeV, together with four
very heavy scalar bosons are predicted.Comment: 11 pages, LATEX, no figures. Talk given at the 2nd Gursey Memorial
Conference, June 2000, Istanbu
W(infty)-Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
The differential structure of operator bases used in various forms of the
Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a
derivative-based approach, alternative to the conventional integral-based one
is developed. Thus the fundamental quantum relations follow in a simpler and
unified manner. An explicit formula for the ordered products of the
Heisenberg-Weyl algebra is obtained. The W(infty) -covariance of the
WWGM-quantization in its most general form is established. It is shown that the
group action of W(infty) that is realized in the classical phase space induces
on bases operators in the corresponding Hilbert space a similarity
transformation generated by the corresponding quantum W(infty) which provides a
projective representation of the former . Explicit expressions for
the algebra generators in the classical phase space and in the Hilbert space
are given. It is made manifest that this W(infty)-covariance of the
WWGM-quantization is a genuine property of the operator bases.Comment: 14 pages, Latex file. No figures. To apear in J. Math. Phy
Monopole equations on 8-manifolds with Spin(7) holonomy
We construct a consistent set of monopole equations on eight-manifolds with
Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions
including all the 4-dimensional Seiberg-Witten solutions as a special case.Comment: 14 pages, LATEX (No figures
The Geometry of Self-dual 2-forms
We show that self-dual 2-forms in 2n dimensional spaces determine a
dimensional manifold and the dimension of the maximal linear
subspaces of is equal to the (Radon-Hurwitz) number of linearly
independent vector fields on the sphere . We provide a direct proof
that for odd has only one-dimensional linear submanifolds.
We exhibit dimensional subspaces in dimensions which are multiples of
, for . In particular, we demonstrate that the seven dimensional
linear subspaces of also include among many other interesting
classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand,
Fairlie and Nuyts and a representation of
given by octonionic multiplication. We discuss the relation of the linear
subspaces with the representations of Clifford algebras.Comment: Latex, 15 page
An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions
We examine the axi-dilatonic sector of low energy string theory and
demonstrate how the gravitational interactions involving the axion and dilaton
fields may be derived from a geometrical action principle involving the
curvature scalar associated with a non-Riemannian connection. In this geometry
the antisymmetric tensor 3-form field determines the torsion of the connection
on the frame bundle while the gradient of the metric is determined by the
dilaton field. By expressing the theory in terms of the Levi-Civita connection
associated with the metric in the ``Einstein frame'' we confirm that the field
equations derived from the non-Riemannian Einstein-Hilbert action coincide with
the axi-dilaton sector of the low energy effective action derived from string
theory.Comment: 6 pages Plain Tex (No Figures), Letter to Editor Classical and
Quantum Gravit
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