175 research outputs found
Muon capture on light nuclei
This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and
3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising
from the axial two-body currents obtained imposing the
partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2
and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon
potential, in combination with the Urbana IX three-nucleon potential in the
case of A=3. The weak current consists of vector and axial components derived
in chiral effective field theory. The low-energy constant entering the vector
(axial) component is determined by reproducting the isovector combination of
the trinucleon magnetic moment (Gamow-Teller matrix element of tritium
beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9)
s^{-1} for A=3, where the uncertainties arise from the adopted fitting
procedure.Comment: 6 pages, submitted to Few-Body Sys
Yang-Mills theory for bundle gerbes
Given a bundle gerbe with connection on an oriented Riemannian manifold of
dimension at least equal to 3, we formulate and study the associated Yang-Mills
equations. When the Riemannian manifold is compact and oriented, we prove the
existence of instanton solutions to the equations and also determine the moduli
space of instantons, thus giving a complete analysis in this case. We also
discuss duality in this context.Comment: Latex2e, 7 pages, some typos corrected, to appear in J. Phys. A:
Math. and Ge
Non-Abelian Tensor Multiplet Equations from Twistor Space
We establish a Penrose-Ward transform yielding a bijection between
holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual
tensor fields on six-dimensional flat space-time. Extending the twistor space
to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0)
supersymmetric non-Abelian constraint equations containing the tensor
multiplet. We also demonstrate how this construction leads to constraint
equations for non-Abelian supersymmetric self-dual strings.Comment: v3: 23 pages, revised version published in Commun. Math. Phy
A Kaehler Structure on the Space of String World-Sheets
Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of
oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with
fixed boundary conditions. Then the infinite-dimensional manifold S carries a
natural complex structure and a compatible (positive-definite) Kaehler metric h
on S determined by the Lorentz metric g. Similar results are proved for other
dimensions and signatures, thus generalizing results of Brylinski regarding
knots in 3-manifolds. Generalizing the framework of Lempert, we also
investigate the precise sense in which S is an infinite-dimensional complex
manifold.Comment: 13 pages, LaTe
BRST, anti-BRST and their geometry
We continue the comparison between the field theoretical and geometrical
approaches to the gauge field theories of various types, by deriving their
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and
comparing them with the geometrical properties of the bundles and gerbes. In
particular, we provide the geometrical interpretation of the so--called
Curci-Ferrari conditions that are invoked for the absolute anticommutativity of
the BRST and anti-BRST symmetry transformations in the context of non-Abelian
1-form gauge theories as well as Abelian gauge theory that incorporates a
2-form gauge field. We also carry out the explicit construction of the 3-form
gauge fields and compare it with the geometry of 2--gerbes.Comment: A comment added. To appear in Jour. Phys. A: Mathemaical and
Theoretica
Quantum circuits with uniformly controlled one-qubit gates
Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some
result
A Coboundary Morphism For The Grothendieck Spectral Sequence
Given an abelian category with enough injectives we show that a
short exact sequence of chain complexes of objects in gives rise
to a short exact sequence of Cartan-Eilenberg resolutions. Using this we
construct coboundary morphisms between Grothendieck spectral sequences
associated to objects in a short exact sequence. We show that the coboundary
preserves the filtrations associated with the spectral sequences and give an
application of these result to filtrations in sheaf cohomology.Comment: 18 page
On the algebraic index for riemannian \'etale groupoids
In this paper we construct an explicit quasi-isomorphism to study the cyclic
cohomology of a deformation quantization over a riemannian \'etale groupoid.
Such a quasi-isomorphism allows us to propose a general algebraic index problem
for riemannian \'etale groupoids. We discuss solutions to that index problem
when the groupoid is proper or defined by a constant Dirac structure on a 3-dim
torus.Comment: 19 page
On Twistors and Conformal Field Theories from Six Dimensions
We discuss chiral zero-rest-mass field equations on six-dimensional
space-time from a twistorial point of view. Specifically, we present a detailed
cohomological analysis, develop both Penrose and Penrose-Ward transforms, and
analyse the corresponding contour integral formulae. We also give twistor space
action principles. We then dimensionally reduce the twistor space of
six-dimensional space-time to obtain twistor formulations of various theories
in lower dimensions. Besides well-known twistor spaces, we also find a novel
twistor space amongst these reductions, which turns out to be suitable for a
twistorial description of self-dual strings. For these reduced twistor spaces,
we explain the Penrose and Penrose-Ward transforms as well as contour integral
formulae.Comment: v4: 66 pages, typos fixed, appendix B revise
Cavity QED and Quantum Computation in the Weak Coupling Regime
In this paper we consider a model of quantum computation based on n atoms of
laser-cooled and trapped linearly in a cavity and realize it as the n atoms
Tavis-Cummings Hamiltonian interacting with n external (laser) fields.
We solve the Schr{\" o}dinger equation of the model in the case of n=2 and
construct the controlled NOT gate by making use of a resonance condition and
rotating wave approximation associated to it. Our method is not heuristic but
completely mathematical, and the significant feature is a consistent use of
Rabi oscillations.
We also present an idea of the construction of three controlled NOT gates in
the case of n=3 which gives the controlled-controlled NOT gate.Comment: Latex file, 22 pages, revised version. To appear in Journal of Optics
B : Quantum and Semiclassical Optic
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