A generalized Fourier inversion theorem

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained by Ruy Exel in the case of Abelian groups.Comment: 15 pages; some typos correcte

Localization via Automorphisms of the CARs. Local gauge invariance

The classical matter fields are sections of a vector bundle E with base manifold M. The space L^2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of C_b^\infty(M) on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra A, of the canonical anticommutation relations on L^2(E), with which we can perform the analogous localization. That is, the net structure of the CAR, A, w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps. As a corollary, we prove a well-known "folk theorem," that the algebra A contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E.Comment: 15 page

Simultaneous saccharification and fermentation of steam exploded duckweed: Improvement of the ethanol yield by increasing yeast titre

This study investigated the conversion of Lemna minor biomass to bioethanol. The biomass was pre-treated by steam explosion (SE, 210 °C, 10 min) and then subjected to simultaneous saccharification and fermentation (SSF) using CellicÒ CTec 2 (20 U or 0.87 FPU gﰂ1 substrate) cellulase plus b-glucosidase (2 U gﰂ1 substrate) and a yeast inoculum of 10% (v/v or 8.0 ﰀ 107 cells mLﰂ1). At a substrate concentration of 1% (w/v) an ethanol yield of 80% (w/w, theoretical) was achieved. However at a substrate concentration of 20% (w/v), the ethanol yield was lowered to 18.8% (w/w, theoretical). Yields were considerably improved by increasing the yeast titre in the inoculum or preconditioning the yeast on steam exploded liquor. These approaches enhanced the ethanol yield up to 70% (w/w, theoretical) at a substrate concen- tration of 20% (w/v) by metabolising fermentation inhibitors

The quantum structure of spacetime at the Planck scale and quantum fields

We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS^2 of the 2-sphere. The relations with Connes' theory of the standard model will be studied elsewhere.Comment: TeX, 37 pages. Since recent and forthcoming articles (hep-th/0105251, hep-th/0201222, hep-th/0301100) are based on this paper, we thought it would be convenient for the readers to have it available on the we

Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.Comment: 34 page

Continuous Spectrum of Automorphism Groups and the Infraparticle Problem

This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical Physic

Almost commuting unitary matrices related to time reversal

The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the mathematical behavior of almost commuting Hermitian matrices to depend on two factors. One factor will be the approximate polynomial relations satisfied by the matrices. The other factor is what algebra the matrices are in, either the matrices over A for A the real numbers, A the complex numbers or A the algebra of quaternions. There are potential obstructions keeping k-tuples of almost commuting operators from being close to a commuting k-tuple. We consider two-dimensional geometries and so this obstruction lives in KO_{-2}(A). This obstruction corresponds to either the Chern number or spin Chern number in physics. We show that if this obstruction is the trivial element in K-theory then the approximation by commuting matrices is possible.Comment: 33 pages, 2 figures. In version 2 some formulas have been corrected and some proofs have been rewritten to improve the expositio

The Levi Problem On Strongly Pseudoconvex GG-Bundles

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by holomorphic transformations satisfying a local property, then the space of square-integrable holomorphic functions on $M$ is infinite $G$-dimensional.Comment: 19 pages--Corrects earlier version

Subclinical leaflet thrombosis after transcatheter aortic valve implantation: no association with left ventricular reverse remodeling at 1-year follow-up

Hypo-attenuated leaflet thickening (HALT) of transcatheter aortic valves is detected on multidetector computed tomography (MDCT) and reflects leaflet thrombosis. Whether HALT affects left ventricular (LV) reverse remodeling, a favorable effect of LV afterload reduction after transcatheter aortic valve implantation (TAVI) is unknown. The aim of this study was to examine the association of HALT after TAVI with LV reverse remodeling. In this multicenter case-control study, patients with HALT on MDCT were identified, and patients without HALT were propensity matched for valve type and size, LV ejection fraction (LVEF), sex, age and time of scan. LV dimensions and function were assessed by transthoracic echocardiography before and 12 months after TAVI. Clinical outcomes (stroke or transient ischemic attack, heart failure hospitalization, new-onset atrial fibrillation, all-cause mortality) were recorded. 106 patients (age 81 +/- 7 years, 55% male) with MDCT performed 37 days [IQR 32-52] after TAVI were analyzed (53 patients with HALT and 53 matched controls). Before TAVI, all echocardiographic parameters were similar between the groups. At 12 months follow-up, patients with and without HALT showed a significant reduction in LV end-diastolic volume, LV end-systolic volume and LV mass index (from 125 +/- 37 to 105 +/- 46 g/m(2), p = 0.001 and from 127 +/- 35 to 101 +/- 27 g/m(2), p < 0.001, respectively, p for interaction = 0.48). Moreover, LVEF improved significantly in both groups. In addition, clinical outcomes were not statistically different. Improvement in LVEF and LV reverse remodeling at 12 months after TAVI were not limited by HALT.Cardiolog