57,365 research outputs found
Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
We review some recent progress in quantum field theory in non-commutative
space, focusing onto the fuzzy sphere as a non-perturbative regularisation
scheme. We first introduce the basic formalism, and discuss the limits
corresponding to different commutative or non-commutative spaces. We present
some of the theories which have been investigated in this framework, with a
particular attention to the scalar model. Then we comment on the results
recently obtained from Monte Carlo simulations, and show a preview of new
numerical data, which are consistent with the expected transition between two
phases characterised by the topology of the support of a matrix eigenvalue
distribution.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
The Pondicherry interpretation of quantum mechanics: An overview
An overview of the Pondicherry interpretation of quantum mechanics is
presented. This interpretation proceeds from the recognition that the
fundamental theoretical framework of physics is a probability algorithm, which
serves to describe an objective fuzziness (the literal meaning of Heisenberg's
term "Unschaerfe," usually mistranslated as "uncertainty") by assigning
objective probabilities to the possible outcomes of unperformed measurements.
Although it rejects attempts to construe quantum states as evolving ontological
states, it arrives at an objective description of the quantum world that owes
nothing to observers or the goings-on in physics laboratories. In fact, unless
such attempts are rejected, quantum theory's true ontological implications
cannot be seen. Among these are the radically relational nature of space, the
numerical identity of the corresponding relata, the incomplete spatiotemporal
differentiation of the physical world, and the consequent top-down structure of
reality, which defies attempts to model it from the bottom up, whether on the
basis of an intrinsically differentiated spacetime manifold or out of a
multitude of individual building blocks.Comment: 18 pages, 1 eps figure, v3: with corrections made in proo
Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model
We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time
and representing the spatial part on a fuzzy sphere. The latter involves a
truncated expansion of the field in spherical harmonics. This yields a
numerically tractable formulation, which constitutes an unconventional
alternative to the lattice. In contrast to the 2d version, the radius R plays
an independent r\^{o}le. We explore the phase diagram in terms of R and the
cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases
of disorder, uniform order and non-uniform order. We compare the result to the
phase diagrams of the 3d model on a non-commutative torus, and of the 2d model
on a fuzzy sphere. Our data at strong coupling reproduce accurately the
behaviour of a matrix chain, which corresponds to the c=1-model in string
theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure
Simulation of Water Distribution Systems
In this paper a software package offering a means of simulating
complex water distribution systems is described. It has been
developed in the course of our investigations into the applicability
of neural networks and fuzzy systems for the implementation of
decision support systems in operational control of industrial
processes with case-studies taken from the water industry.
Examples of how the simulation package have been used in a
design and testing of the algorithms for state estimation,
confidence limit analysis and fault detection are presented.
Arguments for using a suitable graphical visualization techniques
in solving problems like meter placement or leakage diagnosis are
also given and supported by a set of examples
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