Monopole-charge instability

For monopoles with nonvanishing Higgs potential it is shown that with respect to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to that of a pure gauge theory on the two-sphere (b) each topological sector admits one, and only one, stable monopole charge, and (c) each unstable monopole admits $2\sum_{q<0} (2|q|-1)$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the 2-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres. The general theory is illustrated for the little groups U(2), U(3), SU(3)/Z_3 and O(5).Comment: LaTex, 38 pages. 7 figures and 2 photos. Posted for the record. Originally published 20 years ago, with Note added in 2009: Hommage to Lochlainn O'Raifeartaigh and Sidney Coleman. Some typos correcte

Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The associated quantum algebra consists of functions affine in action coordinates. We obtain a set of its nonequivalent representations in the separable pre-Hilbert space of smooth complex functions on the torus where action operators and a Hamiltonian are diagonal and have countable spectra.Comment: 8 page

Toeplitz Quantization of K\"ahler Manifolds and gl(N)gl(N) N→∞N\to\infty

For general compact K\"ahler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras $gl(N)$, $N\to\infty$.Comment: 17 pages, AmsTeX 2.1, Sept. 93 (rev: only typos are corrected

Bergman Kernel from Path Integral

We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kahler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.Comment: 27 page

Performance of the new SPS beam position orbit system (MOPOS)

The orbit and trajectory measurement system COPOS of the CERN SPS accelerator has been in operation since the construction of the machine in 1976. Over the years the system has been slightly modified in order to follow the evolving demands of the machine, in particular for its operation as a p-pbar collider and, since 1991, for the acceleration of heavy ions. In 1995 the performance of the system was reviewed and the following shortcomings were identified: - lack of turn-by-turn position measurements due to the 1ms integration time of the voltage to frequency converters used for the analogue to digital conversion (to be compared with a revolution time of 23 ms), - ageing effects on the 200 MHz resonating input filters, which had over the years drifted out of tolerance. As a consequence the signal to noise ratio, the linearity and the absolute precision were affected, - the calibration system based on electromechanical relays had become very unreliable, such that frequent calibrations were no longer possible, - a remote diagnostic for the observation of timing signals relative to the beam signals was missing. For the above reasons a large-scale upgrade program was launched, the results of which are described in the following sections

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio

Platelets mediate lymphovenous hemostasis to maintain blood-lymphatic separation throughout life

Mammals transport blood through a high-pressure, closed vascular network and lymph through a low-pressure, open vascular network. These vascular networks connect at the lymphovenous (LV) junction, where lymph drains into blood and an LV valve (LVV) prevents backflow of blood into lymphatic vessels. Here we describe an essential role for platelets in preventing blood from entering the lymphatic system at the LV junction. Loss of CLEC2, a receptor that activates platelets in response to lymphatic endothelial cells, resulted in backfilling of the lymphatic network with blood from the thoracic duct (TD) in both neonatal and mature mice. Fibrin-containing platelet thrombi were observed at the LVV and in the terminal TD in wild-type mice, but not Clec2-deficient mice. Analysis of mice lacking LVVs or lymphatic valves revealed that platelet-mediated thrombus formation limits LV backflow under conditions of impaired valve function. Examination of mice lacking integrin-mediated platelet aggregation indicated that platelet aggregation stabilizes thrombi that form in the lymphatic vascular environment to prevent retrograde blood flow. Collectively, these studies unveil a newly recognized form of hemostasis that functions with the LVV to safeguard the lymphatic vascular network throughout life

Quantum Magnetic Algebra and Magnetic Curvature

The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of Weyl-symmetrized functions in coordinate and momentum operators satisfying nonlinear commutation relations. The multiplication in this algebra generates an associative product of functions on the phase space. This product is given by an integral kernel whose phase is the symplectic area of a groupoid-consistent membrane. A symplectic phase space connection with non-trivial curvature is extracted from the magnetic reflections associated with the Stratonovich quantizer. Zero and constant curvature cases are considered as examples. The quantization with both static and time dependent electromagnetic fields is obtained. The expansion of the product by the deformation parameter, written in the covariant form, is compared with the known deformation quantization formulas.Comment: 23 page

Contact Manifolds, Contact Instantons, and Twistor Geometry

Recently, Kallen and Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation. Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties. We also present certain extensions to higher dimensions and supersymmetric generalisations.Comment: v3: 28 pages, clarifications and references added, version to appear in JHE