743 research outputs found
Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector
The quantisation of gauge invariant systems usually proceeds through some
gauge fixing procedure of one type or another. Typically for most cases, such
gauge fixings are plagued by Gribov ambiguities, while it is only for an
admissible gauge fixing that the correct dynamical description of the system is
represented, especially with regards to non perturbative phenomena. However,
any gauge fixing procedure whatsoever may be avoided altogether, by using
rather a recently proposed new approach based on the projection operator onto
physical gauge invariant states only, which is necessarily free on any such
issues. These different aspects of gauge invariant systems are explicitely
analysed within a solvable U(1) gauge invariant quantum mechanical model
related to the dimensional reduction of Yang-Mills theory.Comment: 22 pages, no figures, plain LaTeX fil
Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra
The general construction of self-adjoint configuration space representations
of the Heisenberg algebra over an arbitrary manifold is considered. All such
inequivalent representations are parametrised in terms of the topology classes
of flat U(1) bundles over the configuration space manifold. In the case of
Riemannian manifolds, these representations are also manifestly diffeomorphic
covariant. The general discussion, illustrated by some simple examples in non
relativistic quantum mechanics, is of particular relevance to systems whose
configuration space is parametrised by curvilinear coordinates or is not simply
connected, which thus include for instance the modular spaces of theories of
non abelian gauge fields and gravity.Comment: 22 pages, no figures, plain LaTeX file; changes only in details of
affiliation and financial suppor
The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane
The N=1 supersymmetric invariant Landau problem is constructed and solved. By
considering Landau level projections remaining non trivial under N=1
supersymmetry transformations, the algebraic structures of the N=1
supersymmetric covariant non(anti)commutative superplane analogue of the
ordinary N=0 noncommutative Moyal-Voros plane are identified
Finite Euler Hierarchies And Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively
constructed {}from their successive equations of motion is briefly reviewed. On
the one hand, a certain triality structure is described, relating arbitrary
field theories, {\it classical\ts} topological field theories -- whose
classical solutions span topological classes of manifolds -- and
reparametrisation invariant theories -- generalising ordinary string and
membrane theories. On the other hand, {\it finite} Euler hierarchies are
constructed for all three classes of theories. These hierarchies terminate with
{\it universal\ts} equations of motion, probably defining new integrable
systems as they admit an infinity of Lagrangians. Speculations as to the
possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p.,
(Plain TeX), DTP-92/3
Ostrogradsky's Hamilton formalism and quantum corrections
By means of a simple scalar field theory it is demonstrated that the Lagrange
formalism and Ostrogradsky's Hamilton formalism in the presence of higher
derivatives, in general, do not lead to the same results. While the two
approaches are equivalent at the classical level, differences appear due to the
quantum corrections.Comment: 10 pages, 1 figure, REVTeX
Spectrum of the non-commutative spherical well
We give precise meaning to piecewise constant potentials in non-commutative
quantum mechanics. In particular we discuss the infinite and finite
non-commutative spherical well in two dimensions. Using this, bound-states and
scattering can be discussed unambiguously. Here we focus on the infinite well
and solve for the eigenvalues and eigenfunctions. We find that time reversal
symmetry is broken by the non-commutativity. We show that in the commutative
and thermodynamic limits the eigenstates and eigenfunctions of the commutative
spherical well are recovered and time reversal symmetry is restored
Gauge Fixing and BFV Quantization
Nonsingularity conditions are established for the BFV gauge-fixing fermion
which are sufficient for it to lead to the correct path integral for a theory
with constraints canonically quantized in the BFV approach. The conditions
ensure that anticommutator of this fermion with the BRST charge regularises the
path integral by regularising the trace over non-physical states in each ghost
sector. The results are applied to the quantization of a system which has a
Gribov problem, using a non-standard form of the gauge-fixing fermion.Comment: 14 page
Risk factors of infection and molecular typing in ICU colonized patients with Enterobacter aerogenes
Toward Automatic Interpretation of Narrative Feedback in Competency-Based Portfolios
Self-directed learning is generally considered a key competence in higher education. To enable self-directed learning, assessment practices increasingly embrace assessment for learning rather than the assessment of learning, shifting the focus from grades and scores to provision of rich, narrative, and personalized feedback. Students are expected to collect, interpret, and give meaning to this feedback, in order to self-assess their progress and to formulate new, appropriate learning goals and strategies. However, interpretation of aggregated, longitudinal narrative feedback has been proven to be very challenging, cognitively demanding, and time consuming. In this article, we, therefore, explored the applicability of existing, proven text mining techniques to support feedback interpretation. More specifically, we investigated whether it is possible to automatically generate meaningful information about prevailing topics and the emotional load of feedback provided in medical students' competence-based portfolios (N = 1500), taking into account the competence framework and the students' various performance levels. Our findings indicate that the text-mining techniques topic modeling and sentiment analysis make it feasible to automatically unveil the two principal aspects of narrative feedback, namely the most relevant topics in the feedback and their sentiment. This article, therefore, takes a valuable first step toward the automatic, online support of students, who are tasked with meaningful interpretation of complex narrative data in their portfolio as they develop into self-directed life-long learners
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