942 research outputs found
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
Noncentral extensions as anomalies in classical dynamical systems
A two cocycle is associated to any action of a Lie group on a symplectic
manifold. This allows to enlarge the concept of anomaly in classical dynamical
systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001)
518-533] so as to encompass some extensions of Lie algebras related to
noncanonical actions.Comment: arxiv version is already officia
Abelian BF theory and Turaev-Viro invariant
The U(1) BF Quantum Field Theory is revisited in the light of
Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition
function is related to the BF one and how the latter on its turn coincides with
an abelian Turaev-Viro invariant. Significant differences compared to the
non-abelian case are highlighted.Comment: 47 pages and 6 figure
Geometrical aspects of integrable systems
We review some basic theorems on integrability of Hamiltonian systems, namely
the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem
on partial integrability and the Mishchenko-Fomenko theorem on noncommutative
integrability, and for each of them we give a version suitable for the
noncompact case. We give a possible global version of the previous local
results, under certain topological hypotheses on the base space. It turns out
that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in
Modern Physics vol.5 n.3 (May 2008) issu
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
Unitary evolution of free massless fields in de Sitter space-time
We consider the quantum dynamics of a massless scalar field in de Sitter
space-time. The classical evolution is represented by a canonical
transformation on the phase space for the field theory. By studying the
corresponding Bogoliubov transformations, we show that the symplectic map that
encodes the evolution between two instants of time cannot be unitarily
implemented on any Fock space built from a SO(4)-symmetric complex structure.
We will show also that, in contrast with some effectively lower dimensional
examples arising from Quantum General Relativity such as Gowdy models, it is
impossible to find a time dependent conformal redefinition of the massless
scalar field leading to a quantum unitary dynamics.Comment: 20 pages. Comments and references adde
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
Quantum Attractor Flows
Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a
holographic correspondence in the mini-superspace approximation, we study the
radial quantization of stationary, spherically symmetric black holes in four
dimensions. A key ingredient is the classical equivalence between the radial
evolution equation and geodesic motion of a fiducial particle on the moduli
space M^*_3 of the three-dimensional theory after reduction along the time
direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler
manifold; in this case, we show that BPS black holes correspond to a particular
class of geodesics which lift holomorphically to the twistor space Z of M^*_3,
and identify Z as the BPS phase space. We give a natural quantization of the
BPS phase space in terms of the sheaf cohomology of Z, and compute the exact
wave function of a BPS black hole with fixed electric and magnetic charges in
this framework. We comment on the relation to the topological string amplitude,
extensions to N>2 supergravity theories, and applications to automorphic black
hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published
version, minor change
Hamiltonian thermodynamics of the Reissner-Nordstr\"om-anti-de Sitter black hole
We consider the Hamiltonian dynamics and thermodynamics of spherically
symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We
impose boundary conditions that enforce every classical solution to be an
exterior region of a Reissner-Nordstr\"om-anti-de Sitter black hole with a
nondegenerate Killing horizon, with the spacelike hypersurfaces extending from
the horizon bifurcation two-sphere to the asymptotically anti-de Sitter
infinity. The constraints are simplified by a canonical transformation, which
generalizes that given by Kucha\v{r} in the spherically symmetric vacuum
Einstein theory, and the theory is reduced to its true dynamical degrees of
freedom. After quantization, the grand partition function of a thermodynamical
grand canonical ensemble is obtained by analytically continuing the Lorentzian
time evolution operator to imaginary time and taking the trace. A~similar
analysis under slightly modified boundary conditions leads to the partition
function of a thermodynamical canonical ensemble. The thermodynamics in each
ensemble is analyzed, and the conditions that the (grand) partition function be
dominated by a classical Euclidean black hole solution are found. When these
conditions are satisfied, we recover in particular the Bekenstein-Hawking
entropy. The limit of a vanishing cosmological constant is briefly discussed.
(This paper is dedicated to Karel Kucha\v{r} on the occasion of his sixtieth
birthday.)Comment: 34 pages, REVTeX v3.0. (Minor corrections and presentational
revisions; added references.
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