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Regularization of gravity theories and local Lorentz transformation
We regularized the field equations of gravity theories such that the
effect of Local Lorentz Transformation (LLT), in the case of spherical
symmetry, is removed. A "general tetrad field", with an arbitrary function of
radial coordinate preserving spherical symmetry is provided. We split that
tetrad field into two matrices; the first represents a LLT, which contains an
arbitrary function, the second matrix represents a proper tetrad field which is
a solution to the field equations of gravitational theory, (which are
not invariant under LLT). This "general tetrad field" is then applied to the
regularized field equations of . We show that the effect of the arbitrary
function which is involved in the LLT invariably disappears.Comment: 12 page
Grover Algorithm with zero theoretical failure rate
In standard Grover's algorithm for quantum searching, the probability of
finding the marked item is not exactly 1. In this Letter we present a modified
version of Grover's algorithm that searches a marked state with full successful
rate. The modification is done by replacing the phase inversion by two phase
rotation through angle . The rotation angle is given analytically to be
, where
, the number of items in the database, and
an integer equal to or greater than the integer part of . Upon measurement at -th iteration, the marked state
is obtained with certainty.Comment: 5 pages. Accepted for publication in Physical Review
On the Regularization of Kerr-NUT spacetime: I
Within the framework of teleparallel equivalent of general relativity (TEGR)
theory, calculation of the total energy and momentum of Kerr-NUT spacetimes
have been employed using two methods of the gravitational energy-momentum,
which is coordinate independent, and the Riemannian connection 1-form,
. It has been shown that the two methods
give the same an unacceptable result, i.e., divergent value. Therefore, a local
Lorentz transformation that plays a role of a regularizing tool, which
subtracts the inertial effects without distorting the true gravitational
contribution, has been suggested. This transformation keeps the resulting
spacetime to be a solution of the equations of motion of TEGR.Comment: 10 pages, Latex (Will appear in Prog. Theor. Phys.
Schwarzschild solution in extended teleparallel gravity
Tetrad field, with two unknown functions of radial coordinate and an angle
which is the polar angle times a function of the redial
coordinate, is applied to the field equation of modified theory of gravity.
Exact vacuum solution is derived whose scalar torsion, , is constant. When the angle coincides with the
polar angle , the derived solution will be a solution only for linear
form of gravitational theory.Comment: 8 pages Late
A Rejoinder on Quaternionic Projective Representations
In a series of papers published in this Journal (J. Math. Phys.), a
discussion was started on the significance of a new definition of projective
representations in quaternionic Hilbert spaces. The present paper gives what we
believe is a resolution of the semantic differences that had apparently tended
to obscure the issues.Comment: AMStex, 6 Page
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