206 research outputs found
Quantum diagonalization of Hermitean matrices
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (N ×N) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the `collapse of the wavefunction' associated with a measurement, the procedure is neither a digital nor an analogue calculation - it defines thus a new example of a quantum mechanical method of computation
SIC-POVMs and the Extended Clifford Group
We describe the structure of the extended Clifford Group (defined to be the
group consisting of all operators, unitary and anti-unitary, which normalize
the generalized Pauli group (or Weyl-Heisenberg group as it is often called)).
We also obtain a number of results concerning the structure of the Clifford
Group proper (i.e. the group consisting just of the unitary operators which
normalize the generalized Pauli group). We then investigate the action of the
extended Clifford group operators on symmetric informationally complete POVMs
(or SIC-POVMs) covariant relative to the action of the generalized Pauli group.
We show that each of the fiducial vectors which has been constructed so far
(including all the vectors constructed numerically by Renes et al) is an
eigenvector of one of a special class of order 3 Clifford unitaries. This
suggests a strengthening of a conjuecture of Zauner's. We give a complete
characterization of the orbits and stability groups in dimensions 2-7. Finally,
we show that the problem of constructing fiducial vectors may be expected to
simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We
illustrate this point by constructing exact expressions for fiducial vectors in
dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's
original conjecture, and an alternative, possibly stronger version of the
conjecture in version 1 of this paper; also a few other minor improvement
Calculation of two-loop virtual corrections to b --> s l+ l- in the standard model
We present in detail the calculation of the virtual O(alpha_s) corrections to
the inclusive semi-leptonic rare decay b --> s l+ l-. We also include those
O(alpha_s) bremsstrahlung contributions which cancel the infrared and mass
singularities showing up in the virtual corrections. In order to avoid large
resonant contributions, we restrict the invariant mass squared s of the lepton
pair to the range 0.05 < s/mb^2 < 0.25. The analytic results are represented as
expansions in the small parameters s/mb^2, z = mc^2/mb^2 and s/(4 mc^2). The
new contributions drastically reduce the renormalization scale dependence of
the decay spectrum. For the corresponding branching ratio (restricted to the
above s-range) the renormalization scale uncertainty gets reduced from +/-13%
to +/-6.5%.Comment: 41 pages including 9 postscript figures; in version 2 some typos and
inconsistent notation correcte
Transformation laws of the components of classical and quantum fields and Heisenberg relations
The paper recalls and point to the origin of the transformation laws of the
components of classical and quantum fields. They are considered from the
"standard" and fibre bundle point of view. The results are applied to the
derivation of the Heisenberg relations in quite general setting, in particular,
in the fibre bundle approach. All conclusions are illustrated in a case of
transformations induced by the Poincar\'e group.Comment: 22 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. For
other papers on the same topic, view http://theo.inrne.bas.bg/~bozho/ . arXiv
admin note: significant text overlap with arXiv:0809.017
Complete gluon bremsstrahlung corrections to the process b -> s l+ l-
In a recent paper, we presented the calculation of the order (alpha_s)
virtual corrections to b->s l+ l- and of those bremsstrahlung terms which are
needed to cancel the infrared divergences. In the present paper we work out the
remaining order(alpha_s) bremsstrahlung corrections to b->s l+ l- which do not
suffer from infrared and collinear singularities. These new contributions turn
out to be small numerically. In addition, we also investigate the impact of the
definition of the charm quark mass on the numerical results.Comment: 20 pages including 11 postscript figure
Reconstructing a pure state of a spin s through three Stern-Gerlach measurements: II
The density matrix of a spin s is fixed uniquely if the probabilities to obtain the value s upon measuring n.S are known for 4s(s+1) appropriately chosen directions n in space. These numbers are just the expectation values of the density operator in coherent spin states, and they can be determined in an experiment carried out with a Stern-Gerlach apparatus. Furthermore, the experimental data can be inverted providing thus a parametrization of the statistical operator by 4s(s+1) positive parameters
Differential Calculi on Commutative Algebras
A differential calculus on an associative algebra A is an algebraic analogue
of the calculus of differential forms on a smooth manifold. It supplies A with
a structure on which dynamics and field theory can be formulated to some extent
in very much the same way we are used to from the geometrical arena underlying
classical physical theories and models. In previous work, certain differential
calculi on a commutative algebra exhibited relations with lattice structures,
stochastics, and parametrized quantum theories. This motivated the present
systematic investigation of differential calculi on commutative and associative
algebras. Various results about their structure are obtained. In particular, it
is shown that there is a correspondence between first order differential
calculi on such an algebra and commutative and associative products in the
space of 1-forms. An example of such a product is provided by the Ito calculus
of stochastic differentials.
For the case where the algebra A is freely generated by `coordinates' x^i,
i=1,...,n, we study calculi for which the differentials dx^i constitute a basis
of the space of 1-forms (as a left A-module). These may be regarded as
`deformations' of the ordinary differential calculus on R^n. For n < 4 a
classification of all (orbits under the general linear group of) such calculi
with `constant structure functions' is presented. We analyse whether these
calculi are reducible (i.e., a skew tensor product of lower-dimensional
calculi) or whether they are the extension (as defined in this article) of a
one dimension lower calculus. Furthermore, generalizations to arbitrary n are
obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose
tiling was incorrect in the first version of the paper (p. 14
Gauge Formalism for General Relativity and Fermionic Matter
A new formalism for spinors on curved spaces is developed in the framework of
variational calculus on fibre bundles. The theory has the same structure of a
gauge theory and describes the interaction between the gravitational field and
spinors. An appropriate gauge structure is also given to General Relativity,
replacing the metric field with spin frames. Finally, conserved quantities and
superpotentials are calculated under a general covariant form.Comment: 18 pages, Plain TEX, revision, explicit expression for superpotential
has been adde
Constraints on the Minimal Supergravity Model with Large
In the minimal supergravity model (mSUGRA), as the parameter
increases, the charged Higgs boson and light bottom squark masses decrease,
which can potentially increase contributions from , \tg\tb_j and
\tz_i\tb_j loops in the decay . We update a previous QCD
improved decay calculation to include in addition the effects of
gluino and neutralino loops. We find that in the mSUGRA model, loops involving
charginos also increase, and dominate over , , \tg\tq and
\tz_i\tq contributions for \tan\beta\agt 5-10. We find for large values of
that most of the parameter space of the mSUGRA model for
is ruled out due to too large a value of branching ratio . For and large , most of parameter space is
allowed, although the regions with the least fine-tuning (low and
) are ruled out due to too low a value of . We
compare the constraints from to constraints from the neutralino
relic density, and to expectations for sparticle discovery at LEP2 and the
Fermilab Tevatron colliders. Finally, we show that non-universal GUT
scale soft breaking squark mass terms can enhance gluino loop contributions to
decay rate even if these are diagonal.Comment: 14 page REVTEX file plus 6 PS figure
Discrete Moyal-type representations for a spin
In Moyal’s formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e., by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P or Q symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels that give rise to discrete symbols. Now operators are represented by functions taking values on (2s+1)2 points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism
- …