30,765 research outputs found
Branes and Quantization
The problem of quantizing a symplectic manifold (M,\omega) can be formulated
in terms of the A-model of a complexification of M. This leads to an
interesting new perspective on quantization. From this point of view, the
Hilbert space obtained by quantization of (M,\omega) is the space of (Bcc,B')
strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian
A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M,
and the choice of \omega is encoded in the choice of Bcc. As an example, we
describe from this point of view the representations of the group SL(2,R).
Another application is to Chern-Simons gauge theory.Comment: 70 pp, v2: references adde
Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
This article studies Markovian stochastic motion of a particle on a graph
with finite number of nodes and periodically time-dependent transition rates
that satisfy the detailed balance condition at any time. We show that under
general conditions, the currents in the system on average become quantized or
fractionally quantized for adiabatic driving at sufficiently low temperature.
We develop the quantitative theory of this quantization and interpret it in
terms of topological invariants. By implementing the celebrated Kirchhoff
theorem we derive a general and explicit formula for the average generated
current that plays a role of an efficient tool for treating the current
quantization effects.Comment: 22 pages, 7 figure
Connes' Tangent Groupoid and Strict Quantization
We address one of the open problems in quantization theory recently listed by
Rieffel. By developping in detail Connes' tangent groupoid principle and using
previous work by Landsman, we show how to construct a strict, flabby
quantization, which is moreover an asymptotic morphism and satisfies the
reality and traciality constraints, on any oriented Riemannian manifold. That
construction generalizes the standard Moyal rule. The paper can be considered
as an introduction to quantization theory from Connes' point of view.Comment: LaTeX file, 22 pages (elsart.cls required). Minor changes. Final
version to appear in J. Geom. and Phy
T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
Recently we introduced T-duality in the study of topological insulators, and
used it to show that T-duality trivialises the bulk-boundary correspondence in
2 dimensions. In this paper, we partially generalise these results to higher
dimensions and briefly discuss the 4D quantum Hall effect.Comment: 25 pages. To appear in Ann. Henri Poincar
Comments on the Covariant Sp(2)-Symmetric Lagrangian BRST Formalism
We give a simple geometrical picture of the basic structures of the covariant
symmetric quantization formalism -- triplectic quantization -- recently
suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the
appearance of an even Poisson bracket is not a particular property of
triplectic quantization. Rather, any solution of the classical master equation
generates on a Lagrangian surface of the antibracket an even Poisson bracket.
Also other features of triplectic quantization can be identified with aspects
of conventional Lagrangian BRST quantization without extended BRST symmetry.Comment: 9 pages, LaTe
Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
We present a rigorous quantization scheme that yields a quantum field theory
in general boundary form starting from a linear field theory. Following a
geometric quantization approach in the K\"ahler case, state spaces arise as
spaces of holomorphic functions on linear spaces of classical solutions in
neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions
over spaces of classical solutions in regions of spacetime. We prove the
validity of the TQFT-type axioms of the general boundary formulation under
reasonable assumptions. We also develop the notions of vacuum and coherent
states in this framework. As a first application we quantize evanescent waves
in Klein-Gordon theory
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