207 research outputs found
Berezin Quantization of Gauged WZW and Coset Models
Gauged WZW and coset models are known to be useful to prove holomorphic
factorization of the partition function of WZW and coset models. In this note
we show that these gauged models can be also important to quantize the theory
in the context of the Berezin formalism. For gauged coset models Berezin
quantization procedure also admits a further holomorphic factorization in the
complex structure of the moduli space.Comment: 15+1 pages, no figures, revte
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
Coherent states and geodesics: cut locus and conjugate locus
The intimate relationship between coherent states and geodesics is pointed
out. For homogenous manifolds on which the exponential from the Lie algebra to
the Lie group equals the geodesic exponential, and in particular for symmetric
spaces, it is proved that the cut locus of the point is equal to the set of
coherent vectors orthogonal to . A simple method to calculate the
conjugate locus in Hermitian symmetric spaces with significance in the coherent
state approach is presented. The results are illustrated on the complex
Grassmann manifold.Comment: 19 pages, enlarged version, 14 pages, Latex + some macros from Revtex
+ some AMS font
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
Toeplitz Quantization of K\"ahler Manifolds and
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 ,
.Comment: 17 pages, AmsTeX 2.1, Sept. 93 (rev: only typos are corrected
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
Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.Comment: 29 pages, part 1 of two papers, published versio
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
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