221 research outputs found
Functions of class Ck without derivatives
We describe a general axiomatic way to define functions of class Ck, k ∈ N∪{∞} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds
On Weyl Quantization from geometric Quantization
A. Weinstein has conjectured a nice looking formula for a deformed product of
functions on a hermitian symmetric space of non-compact type. We derive such a
formula for symmetric symplectic spaces using ideas from geometric quantization
and prequantization of symplectic groupoids. We compute the result explicitly
for the natural 2-dimensional symplectic manifolds: the euclidean plane, the
sphere and the hyperbolic plane. For the euclidean plane we obtain the well
known Moyal-Weyl product. The other cases show that Weinstein's original idea
should be interpreted with care. We conclude with comments on the status of our
result.Comment: 11 pages. (v2: corrected a couple of typos
Symplectic connections and Fedosov's quantization on supermanifolds
A (biased and incomplete) review of the status of the theory of symplectic
connections on supermanifolds is presented. Also, some comments regarding
Fedosov's technique of quantization are made.Comment: Submitted to J. of Phys. Conf. Se
Projective Fourier Duality and Weyl Quantization
The Weyl-Wigner correspondence prescription, which makes large use of Fourier
duality, is reexamined from the point of view of Kac algebras, the most general
background for noncommutative Fourier analysis allowing for that property. It
is shown how the standard Kac structure has to be extended in order to
accommodate the physical requirements. An Abelian and a symmetric projective
Kac algebras are shown to provide, in close parallel to the standard case, a
new dual framework and a well-defined notion of projective Fourier duality for
the group of translations on the plane. The Weyl formula arises naturally as an
irreducible component of the duality mapping between these projective algebras.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures.
requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with text
improvements and crucial typos correction
Obstruction Results in Quantization Theory
We define the quantization structures for Poisson algebras necessary to
generalise Groenewold and Van Hove's result that there is no consistent
quantization for the Poisson algebra of Euclidean phase space. Recently a
similar obstruction was obtained for the sphere, though surprising enough there
is no obstruction to the quantization of the torus. In this paper we want to
analyze the circumstances under which such obstructions appear. In this context
we review the known results for the Poisson algebras of Euclidean space, the
sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc
Cotangent bundle quantization: Entangling of metric and magnetic field
For manifolds of noncompact type endowed with an affine connection
(for example, the Levi-Civita connection) and a closed 2-form (magnetic field)
we define a Hilbert algebra structure in the space and
construct an irreducible representation of this algebra in . This
algebra is automatically extended to polynomial in momenta functions and
distributions. Under some natural conditions this algebra is unique. The
non-commutative product over is given by an explicit integral
formula. This product is exact (not formal) and is expressed in invariant
geometrical terms. Our analysis reveals this product has a front, which is
described in terms of geodesic triangles in . The quantization of
-functions induces a family of symplectic reflections in
and generates a magneto-geodesic connection on . This
symplectic connection entangles, on the phase space level, the original affine
structure on and the magnetic field. In the classical approximation,
the -part of the quantum product contains the Ricci curvature of
and a magneto-geodesic coupling tensor.Comment: Latex, 38 pages, 5 figures, minor correction
Comparison of laparoscopic versus robot-assisted versus transanal total mesorectal excision surgery for rectal cancer:a retrospective propensity score-matched cohort study of short-term outcomes
BACKGROUND: Laparoscopic total mesorectal excision (TME) surgery for rectal cancer has important technical limitations. Robot-assisted and transanal TME (TaTME) may overcome these limitations, potentially leading to lower conversion rates and reduced morbidity. However, comparative data between the three approaches are lacking. The aim of this study was to compare short-term outcomes for laparoscopic TME, robot-assisted TME and TaTME in expert centres. METHODS: Patients undergoing rectal cancer surgery between 2015 and 2017 in expert centres for laparoscopic, robot-assisted or TaTME were included. Outcomes for TME surgery performed by the specialized technique in the expert centres were compared after propensity score matching. The primary outcome was conversion rate. Secondary outcomes were morbidity and pathological outcomes. RESULTS: A total of 1078 patients were included. In rectal cancer surgery in general, the overall rate of primary anastomosis was 39.4, 61.9 and 61.9 per cent in laparoscopic, robot-assisted and TaTME centres respectively (P < 0.001). For specialized techniques in expert centres excluding abdominoperineal resection (APR), the rate of primary anastomosis was 66.7 per cent in laparoscopic, 89.8 per cent in robot-assisted and 84.3 per cent in TaTME (P < 0.001). Conversion rates were 3.7 , 4.6 and 1.9 per cent in laparoscopic, robot-assisted and TaTME respectively (P = 0.134). The number of incomplete specimens, circumferential resection margin involvement rate and morbidity rates did not differ. CONCLUSION: In the minimally invasive treatment of rectal cancer more primary anastomoses are created in robotic and TaTME expert centres
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