518 research outputs found
Breaking the silence of the 500-year-old smiling garden of everlasting flowers: The En Tibi book herbarium
We reveal the enigmatic origin of one of the earliest surviving botanical collections. The 16th-century Italian En Tibi herbarium is a large, luxurious book with c. 500 dried plants, made in the Renaissance scholarly circles that developed botany as a distinct discipline. Its Latin inscription, translated as “Here for you a smiling garden of everlasting flowers”, suggests that this herbarium was a gift for a patron of the emerging botanical science. We follow an integrative approach that includes a botanical similarity estimation of the En Tibi with contemporary herbaria (Aldrovandi, Cesalpino, “Cibo”, Merini, Estense) and analysis of the book’s watermark, paper, binding, handwriting, Latin inscription and the morphology and DNA of hairs mounted under specimens. Rejecting the previous origin hypothesis (Ferrara, 1542–1544), we show that the En Tibi was made in Bologna around 1558. We attribute the En Tibi herbarium to Francesco Petrollini, a neglected 16th-century botanist, to whom also belongs, as clarified herein, the controversial “Erbario Cibo” kept in Rome. The En Tibi was probably a work on commission for Petrollini, who provided the plant material for the book. Other people were apparently involved in the compilation and offering of this precious gift to a yet unknown person, possibly the Habsburg Emperor Ferdinand I. The En Tibi herbarium is a Renaissance masterpiece of art and science, representing the quest for truth in herbal medicine and botany. Our multidisciplinary approach can serve as a guideline for deciphering other anonymous herbaria, kept safely “hidden” in treasure rooms of universities, libraries and museums
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and
internal signature, by applying in detail the Dirac algorithm to the Palatini
action. While the constraint set of the Palatini action contains second class
constraints, by an appeal to the method of gauge unfixing, we map the second
class system to an equivalent first class system which turns out to be
identical to the first class constraint system obtained via the extension of
the ADM phase space performed in our companion paper. Central to our analysis
is again the appropriate treatment of the simplicity constraint. Remarkably,
the simplicity constraint invariant extension of the Hamiltonian constraint,
that is a necessary step in the gauge unfixing procedure, involves a correction
term which is precisely the one found in the companion paper and which makes
sure that the Hamiltonian constraint derived from the Palatini Lagrangian
coincides with the ADM Hamiltonian constraint when Gauss and simplicity
constraints are satisfied. We therefore have rederived our new connection
formulation of General Relativity from an independent starting point, thus
confirming the consistency of this framework.Comment: 42 pages. v2: Journal version. Some nonessential sign errors in
section 2 corrected. Minor clarification
Loop quantum gravity without the Hamiltonian constraint
We show that under certain technical assumptions, including the existence of
a constant mean curvature (CMC) slice and strict positivity of the scalar
field, general relativity conformally coupled to a scalar field can be
quantised on a partially reduced phase space, meaning reduced only with respect
to the Hamiltonian constraint and a proper gauge fixing. More precisely, we
introduce, in close analogy to shape dynamics, the generator of a local
conformal transformation acting on both, the metric and the scalar field, which
coincides with the CMC gauge condition. A new metric, which is invariant under
this transformation, is constructed and used to define connection variables
which can be quantised by standard loop quantum gravity methods. While it is
hard to address dynamical problems in this framework (due to the complicated
'time' function), it seems, due to good accessibility properties of the CMC
gauge, to be well suited for problems such as the computation of black hole
entropy, where actual physical states can be counted and the dynamics is only
of indirect importance. The corresponding calculation yields the surprising
result that the usual prescription of fixing the Barbero-Immirzi parameter beta
to a constant value in order to obtain the well-known formula S = a(Phi) A/(4G)
does not work for the black holes under consideration, while a recently
proposed prescription involving an analytic continuation of beta to the case of
a self-dual space-time connection yields the correct result. Also, the
interpretation of the geometric operators gets an interesting twist, which
exemplifies the deep relationship between observables and the choice of a time
function and has consequences for loop quantum cosmology.Comment: 8 pages. v2: Journal version. Black hole state counting based on
physical states added. Applications to loop quantum cosmology discussed.
Gauge condition used shown to coincide with CMC gauge. Minor clarifications.
v3: Erroneous topology dependence of the entropy in journal version
corrected, conclusions fixed accordingly. Main results unaffecte
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focussed on the quantisation of the
Rarita-Schwinger sector of Supergravity theories in various dimensions by using
an extension of Loop Quantum Gravity to all spacetime dimensions. In this
paper, we extend this analysis by considering the quantisation of additional
bosonic fields necessary to obtain a complete SUSY multiplet next to graviton
and gravitino in various dimensions. As a generic example, we study concretely
the quantisation of the 3-index photon of 11d SUGRA, but our methods easily
extend to more general p-form fields. Due to the presence of a Chern-Simons
term for the 3-index photon, which is due to local SUSY, the theory is
self-interacting and its quantisation far from straightforward. Nevertheless,
we show that a reduced phase space quantisation with respect to the 3-index
photon Gauss constraint is possible. Specifically, the Weyl algebra of
observables, which deviates from the usual CCR Weyl algebras by an interesting
twist contribution proportional to the level of the Chern-Simons theory, admits
a background independent state of the Narnhofer-Thirring type.Comment: 12 pages. v2: Journal version. Minor clarifications and correction
Field-induced effects in the spin liquid candidate PbCuTeO
PbCuTeO is considered as one of the rare candidate materials for a
three-dimensional quantum spin liquid (QSL). This assessment was based on the
results of various magnetic experiments, performed mainly on polycrystalline
material. More recent measurements on single crystals revealed an even more
exotic behavior, yielding ferroelectric order below , accompanied by distinct lattice distortions, and a somewhat
modified magnetic response which is still consistent with a QSL. Here we report
on low-temperature measurements of various thermodynamic, magnetic and
dielectric properties of single crystalline PbCuTeO in magnetic fields
. The combination of these various probes allows us to
construct a detailed - phase diagram including a ferroelectric phase for
and a -induced magnetic phase at
. These phases are preceded by or coincide with a structural
transition from a cubic high-temperature phase into a distorted non-cubic
low-temperature state. The phase diagram discloses two quantum critical points
(QCPs) in the accessible field range, a ferroelectric QCP at =
and a magnetic QCP at = . Field-induced
lattice distortions, observed in the state at and which are
assigned to the effect of spin-orbit interaction of the Cu-ions, are
considered as the key mechanism by which the magnetic field couples to the
dielectric degrees of freedom in this material
Spin liquid and ferroelectricity close to a quantum critical point in PbCuTe2O6
Geometrical frustration among interacting spins combined with strong quantum
fluctuations destabilize long-range magnetic order in favour of more exotic
states such as spin liquids. By following this guiding principle, a number of
spin liquid candidate systems were identified in quasi-two-dimensional
(quasi-2D) systems. For 3D, however, the situation is less favourable as
quantum fluctuations are reduced and competing states become more relevant.
Here we report a comprehensive study of thermodynamic, magnetic and dielectric
properties on single crystalline and pressed-powder samples of PbCuTeO,
a candidate material for a 3D frustrated quantum spin liquid featuring a
hyperkagome lattice. Whereas the low-temperature properties of the powder
samples are consistent with the recently proposed quantum spin liquid state, an
even more exotic behaviour is revealed for the single crystals. These crystals
show ferroelectric order at , accompanied by
strong lattice distortions, and a modified magnetic response -- still
consistent with a quantum spin liquid -- but with clear indications for quantum
critical behaviour.Comment: 59 pages, 15 figures, This version of the article has been accepted
for publication, after peer review but is not the Version of Record and does
not reflect post-acceptance improvements, or any corrections. The Version of
Record is available onlin
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
In our companion papers, we managed to derive a connection formulation of
Lorentzian General Relativity in D+1 dimensions with compact gauge group
SO(D+1) such that the connection is Poisson commuting, which implies that Loop
Quantum Gravity quantisation methods apply. We also provided the coupling to
standard matter. In this paper, we extend our methods to derive a connection
formulation of a large class of Lorentzian signature Supergravity theories, in
particular 11d SUGRA and 4d, N = 8 SUGRA, which was in fact the motivation to
consider higher dimensions. Starting from a Hamiltonian formulation in the time
gauge which yields a Spin(D) theory, a major challenge is to extend the
internal gauge group to Spin(D+1) in presence of the Rarita-Schwinger field.
This is non trivial because SUSY typically requires the Rarita-Schwinger field
to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana
representations of the Clifford algebra are not available in the same spacetime
dimension for both Lorentzian and Euclidean signature. We resolve the arising
tension and provide a background independent representation of the non trivial
Dirac antibracket *-algebra for the Majorana field which significantly differs
from the analogous construction for Dirac fields already available in the
literature.Comment: 43 pages. v2: Journal version. Some nonessential sign errors in
sections 2 and 3 corrected. Minor clarifications and correction
On the Implementation of the Canonical Quantum Simplicity Constraint
In this paper, we are going to discuss several approaches to solve the
quadratic and linear simplicity constraints in the context of the canonical
formulations of higher dimensional General Relativity and Supergravity
developed in our companion papers. Since the canonical quadratic simplicity
constraint operators have been shown to be anomalous in any dimension D>2,
non-standard methods have to be employed to avoid inconsistencies in the
quantum theory. We show that one can choose a subset of quadratic simplicity
constraint operators which are non-anomalous among themselves and allow for a
natural unitary map of the spin networks in the kernel of these simplicity
constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in
D=3. The linear constraint operators on the other hand are non-anomalous by
themselves, however their solution space will be shown to differ in D=3 from
the expected Ashtekar-Lewandowski Hilbert space. We comment on possible
strategies to make a connection to the quadratic theory. Also, we comment on
the relation of our proposals to existing work in the spin foam literature and
how these works could be used in the canonical theory. We emphasise that many
ideas developed in this paper are certainly incomplete and should be considered
as suggestions for possible starting points for more satisfactory treatments in
the future.Comment: 30 pages, 2 figures. v2: Journal version. Comparison to existing
approaches added. Discussion extended. References added. Sign error in
equation (2.15) corrected. Minor clarifications and correction
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