1,456 research outputs found
Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
The moduli space of solutions to the vortex equations on a Riemann surface
are well known to have a symplectic (in fact K\"{a}hler) structure. We show
this symplectic structure explictly and proceed to show a family of symplectic
(in fact, K\"{a}hler) structures on the moduli space,
parametrised by , a section of a line bundle on the Riemann surface.
Next we show that corresponding to these there is a family of prequantum line
bundles on the moduli space whose curvature is
proportional to the symplectic forms .Comment: 8 page
Quantization Of Cyclotron Motion and Quantum Hall Effect
We present a two dimensional model of IQHE in accord with the cyclotron
motion. The quantum equation of the QHE curve and a new definition of filling
factor are also given.Comment: 13 Pages, Latex, 1 figure, to appear in Europhys. Lett. September
199
Time and Geometric Quantization
In this paper we briefly review the functional version of the Koopman-von
Neumann operatorial approach to classical mechanics. We then show that its
quantization can be achieved by freezing to zero two Grassmannian partners of
time. This method of quantization presents many similarities with the one known
as Geometric Quantization.Comment: Talk given by EG at "Spacetime and Fundamental Interactions: Quantum
Aspects. A conference to honour A.P.Balachandran's 65th birthday
Effective Equations of Motion for Quantum Systems
In many situations, one can approximate the behavior of a quantum system,
i.e. a wave function subject to a partial differential equation, by effective
classical equations which are ordinary differential equations. A general method
and geometrical picture is developed and shown to agree with effective action
results, commonly derived through path integration, for perturbations around a
harmonic oscillator ground state. The same methods are used to describe
dynamical coherent states, which in turn provide means to compute quantum
corrections to the symplectic structure of an effective system.Comment: 31 pages; v2: a new example, new reference
Symplectic Cuts and Projection Quantization
The recently proposed projection quantization, which is a method to quantize
particular subspaces of systems with known quantum theory, is shown to yield a
genuine quantization in several cases. This may be inferred from exact results
established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor
Quantum-Mechanical Dualities on the Torus
On classical phase spaces admitting just one complex-differentiable
structure, there is no indeterminacy in the choice of the creation operators
that create quanta out of a given vacuum. In these cases the notion of a
quantum is universal, i.e., independent of the observer on classical phase
space. Such is the case in all standard applications of quantum mechanics.
However, recent developments suggest that the notion of a quantum may not be
universal. Transformations between observers that do not agree on the notion of
an elementary quantum are called dualities. Classical phase spaces admitting
more than one complex-differentiable structure thus provide a natural framework
to study dualities in quantum mechanics. As an example we quantise a classical
mechanics whose phase space is a torus and prove explicitly that it exhibits
dualities.Comment: New examples added, some precisions mad
Extended diffeomorphism algebras in (quantum) gravitational physics
We construct an explicit representation of the algebra of local
diffeomorphisms of a manifold with realistic dimensions. This is achieved in
the setting of a general approach to the (quantum) dynamics of a physical
system which is characterized by the fundamental role assigned to a basic
underlying symmetry. The developed mathematical formalism makes contact with
the relevant gravitational notions by means of the addition of some extra
structure. The specific manners in which this is accomplished, together with
their corresponding physical interpretation, lead to different gravitational
models. Distinct strategies are in fact briefly outlined, showing the
versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure
Wave propagation in two-dimensional periodic lattices
International audiencePlane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries
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