1,054 research outputs found
Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space
Wigner's quasi-probability distribution function in phase-space is a special
(Weyl) representation of the density matrix. It has been useful in describing
quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum
computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It
is also of importance in signal processing.
Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal,
has only emerged in the last quarter-century: It furnishes a third,
alternative, formulation of Quantum Mechanics, independent of the conventional
Hilbert Space, or Path Integral formulations. In this logically complete and
self-standing formulation, one need not choose sides--coordinate or momentum
space. It works in full phase-space, accommodating the uncertainty principle.
This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure
Dirac brackets from magnetic backgrounds
In symplectic mechanics, the magnetic term describing the interaction between
a charged particle and an external magnetic field has to be introduced by hand.
On the contrary, in generalised complex geometry, such magnetic terms in the
symplectic form arise naturally by means of B-transformations. Here we prove
that, regarding classical phase space as a generalised complex manifold, the
transformation law for the symplectic form under the action of a weak magnetic
field gives rise to Dirac's prescription for Poisson brackets in the presence
of constraints.Comment: 9 page
Area Potentials and Deformation Quantization
Systems built out of N-body interactions, beyond 2-body interactions, are
formulated on the plane, and investigated classically and quantum mechanically
(in phase space). Their Wigner Functions--the density matrices in phase-space
quantization--are given and analyzed.Comment: LaTeX, 7 page
The Harari-Shupe preon model and nonrelativistic quantum phase space
We propose that the whole algebraic structure of the Harari-Shupe rishon
model originates via a Dirac-like linearization of quadratic form x^2+p^2, with
position and momentum satisfying standard commutation relations. The scheme
does not invoke the concept of preons as spin-1/2 subparticles, thus evading
the problem of preon confinement, while fully explaining all symmetries emboded
in the Harari-Shupe model. Furthermore, the concept of quark colour is
naturally linked to the ordering of rishons. Our scheme leads to group
U(1)xSU(3) combined with SU(2), with two of the SU(2) generators not commuting
with reflections. An interpretation of intra-generation quark-lepton
transformations in terms of genuine rotations and reflections in phase space is
proposed
The Vector-Tensor Supermultiplet with Gauged Central Charge
The vector-tensor multiplet is coupled off-shell to an N=2 vector multiplet
such that its central charge transformations are realized locally. A gauged
central charge is a necessary prerequisite for a coupling to supergravity and
the strategy underlying our construction uses the potential for such a coupling
as a guiding principle. The results for the action and transformation rules
take a nonlinear form and necessarily include a Chern-Simons term. After a
duality transformation the action is encoded in a homogeneous holomorphic
function consistent with special geometry.Comment: 8 pages, LATE
A Requirement-centric Approach to Web Service Modeling, Discovery, and Selection
Service-Oriented Computing (SOC) has gained considerable popularity for implementing Service-Based Applications (SBAs) in a flexible\ud
and effective manner. The basic idea of SOC is to understand users'\ud
requirements for SBAs first, and then discover and select relevant\ud
services (i.e., that fit closely functional requirements) and offer\ud
a high Quality of Service (QoS). Understanding usersÂ’ requirements\ud
is already achieved by existing requirement engineering approaches\ud
(e.g., TROPOS, KAOS, and MAP) which model SBAs in a requirement-driven\ud
manner. However, discovering and selecting relevant and high QoS\ud
services are still challenging tasks that require time and effort\ud
due to the increasing number of available Web services. In this paper,\ud
we propose a requirement-centric approach which allows: (i) modeling\ud
usersÂ’ requirements for SBAs with the MAP formalism and specifying\ud
required services using an Intentional Service Model (ISM); (ii)\ud
discovering services by querying the Web service search engine Service-Finder\ud
and using keywords extracted from the specifications provided by\ud
the ISM; and(iii) selecting automatically relevant and high QoS services\ud
by applying Formal Concept Analysis (FCA). We validate our approach\ud
by performing experiments on an e-books application. The experimental\ud
results show that our approach allows the selection of relevant and\ud
high QoS services with a high accuracy (the average precision is\ud
89.41%) and efficiency (the average recall is 95.43%)
Wigner phase space distribution as a wave function
We demonstrate that the Wigner function of a pure quantum state is a wave
function in a specially tuned Dirac bra-ket formalism and argue that the Wigner
function is in fact a probability amplitude for the quantum particle to be at a
certain point of the classical phase space. Additionally, we establish that in
the classical limit, the Wigner function transforms into a classical
Koopman-von Neumann wave function rather than into a classical probability
distribution. Since probability amplitude need not be positive, our findings
provide an alternative outlook on the Wigner function's negativity.Comment: 6 pages and 2 figure
From extended phase space dynamics to fluid theory
We derive a fluid theory for spin-1/2 particles starting from an extended
kinetic model based on a spin-projected density matrix formalism. The evolution
equation for the spin density is found to contain a pressure-like term. We give
an example where this term is important by looking at a linear mode previously
found in a spin kinetic model.Comment: 4 page
Noncommutative effective theory of vortices in a complex scalar field
We derive a noncommutative theory description for vortex configurations in a
complex field in 2+1 dimensions. We interpret the Magnus force in terms of the
noncommutativity, and obtain some results for the quantum dynamics of the
system of vortices in that context
Renormalization Group Functional Equations
Functional conjugation methods are used to analyze the global structure of
various renormalization group trajectories, and to gain insight into the
interplay between continuous and discrete rescaling. With minimal assumptions,
the methods produce continuous flows from step-scaling {\sigma} functions, and
lead to exact functional relations for the local flow {\beta} functions, whose
solutions may have novel, exotic features, including multiple branches. As a
result, fixed points of {\sigma} are sometimes not true fixed points under
continuous changes in scale, and zeroes of {\beta} do not necessarily signal
fixed points of the flow, but instead may only indicate turning points of the
trajectories.Comment: A physical model with a limit cycle added as section IV, along with
reference
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