202 research outputs found
Holomorphic Factorization for a Quantum Tetrahedron
We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of
SU(2)-invariant tensors (intertwiners) and establish a holomorphically
factorized formula for the decomposition of identity in H(j_1,..,j_n).
Interestingly, the integration kernel that appears in the decomposition formula
turns out to be the n-point function of bulk/boundary dualities of string
theory. Our results provide a new interpretation for this quantity as being, in
the limit of large conformal dimensions, the exponential of the Kahler
potential of the symplectic manifold whose quantization gives H(j_1,..,j_n).
For the case n=4, the symplectic manifold in question has the interpretation of
the space of "shapes" of a geometric tetrahedron with fixed face areas, and our
results provide a description for the quantum tetrahedron in terms of
holomorphic coherent states. We describe how the holomorphic intertwiners are
related to the usual real ones by computing their overlap. The semi-classical
analysis of these overlap coefficients in the case of large spins allows us to
obtain an explicit relation between the real and holomorphic description of the
space of shapes of the tetrahedron. Our results are of direct relevance for the
subjects of loop quantum gravity and spin foams, but also add an interesting
new twist to the story of the bulk/boundary correspondence.Comment: 45 pages; published versio
Spurious states in the Faddeev formalism for few-body systems
We discuss the appearance of spurious solutions of few-body equations for
Faddeev amplitudes. The identification of spurious states, i.e., states that
lack the symmetry required for solutions of the Schroedinger equation, as well
as the symmetrization of the Faddeev equations is investigated. As an example,
systems of three and four electrons, bound in a harmonic-oscillator potential
and interacting by the Coulomb potential, are presented.Comment: 11 pages. REVTE
Fermions in three-dimensional spinfoam quantum gravity
We study the coupling of massive fermions to the quantum mechanical dynamics
of spacetime emerging from the spinfoam approach in three dimensions. We first
recall the classical theory before constructing a spinfoam model of quantum
gravity coupled to spinors. The technique used is based on a finite expansion
in inverse fermion masses leading to the computation of the vacuum to vacuum
transition amplitude of the theory. The path integral is derived as a sum over
closed fermionic loops wrapping around the spinfoam. The effects of quantum
torsion are realised as a modification of the intertwining operators assigned
to the edges of the two-complex, in accordance with loop quantum gravity. The
creation of non-trivial curvature is modelled by a modification of the pure
gravity vertex amplitudes. The appendix contains a review of the geometrical
and algebraic structures underlying the classical coupling of fermions to three
dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER
Nuclear Alpha-Particle Condensates
The -particle condensate in nuclei is a novel state described by a
product state of 's, all with their c.o.m. in the lowest 0S orbit. We
demonstrate that a typical -particle condensate is the Hoyle state
( MeV, state in C), which plays a crucial role for
the synthesis of C in the universe. The influence of antisymmentrization
in the Hoyle state on the bosonic character of the particle is
discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle
state, therefore, are predominant. It is conjectured that -particle
condensate states also exist in heavier nuclei, like O,
Ne, etc. For instance the state of O at MeV
is identified from a theoretical analysis as being a strong candidate of a
condensate. The calculated small width (34 keV) of ,
consistent with data, lends credit to the existence of heavier Hoyle-analogue
states. In non-self-conjugated nuclei such as B and C, we discuss
candidates for the product states of clusters, composed of 's,
triton's, and neutrons etc. The relationship of -particle condensation
in finite nuclei to quartetting in symmetric nuclear matter is investigated
with the help of an in-medium modified four-nucleon equation. A nonlinear order
parameter equation for quartet condensation is derived and solved for
particle condensation in infinite nuclear matter. The strong qualitative
difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in
Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck,
(Springer-Verlag, Berlin, 2011
Measurement-based quantum foundations
I show that quantum theory is the only probabilistic framework that permits
arbitrary processes to be emulated by sequences of local measurements. This
supports the view that, contrary to conventional wisdom, measurement should not
be regarded as a complex phenomenon in need of a dynamical explanation but
rather as a primitive -- and perhaps the only primitive -- operation of the
theory.Comment: 8 pages, version to appear in Found. Phy
Comparing proton momentum distributions in and 3 nuclei via H H and He measurements
We report the first measurement of the reaction cross-section
ratios for Helium-3 (He), Tritium (H), and Deuterium (). The
measurement covered a missing momentum range of
MeV, at large momentum transfer (
(GeV)) and , which minimized contributions from non
quasi-elastic (QE) reaction mechanisms. The data is compared with plane-wave
impulse approximation (PWIA) calculations using realistic spectral functions
and momentum distributions. The measured and PWIA-calculated cross-section
ratios for He and H extend to just above the typical nucleon
Fermi-momentum ( MeV) and differ from each other by , while for He/H they agree within the measurement accuracy of
about 3\%. At momenta above , the measured He/H ratios differ from
the calculation by . Final state interaction (FSI) calculations
using the generalized Eikonal Approximation indicate that FSI should change the
He/H cross-section ratio for this measurement by less than 5\%. If
these calculations are correct, then the differences at large missing momenta
between the He/H experimental and calculated ratios could be due to the
underlying interaction, and thus could provide new constraints on the
previously loosely-constrained short-distance parts of the interaction.Comment: 8 pages, 3 figures (4 panels
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