6,161 research outputs found
Nonlocal regularisation of noncommutative field theories
We study noncommutative field theories, which are inherently nonlocal, using
a Poincar\'e-invariant regularisation scheme which yields an effective,
nonlocal theory for energies below a cut-off scale. After discussing the
general features and the peculiar advantages of this regularisation scheme for
theories defined in noncommutative spaces, we focus our attention onto the
particular case when the noncommutativity parameter is inversely proportional
to the square of the cut-off, via a dimensionless parameter . We work out
the perturbative corrections at one-loop order for a scalar theory with quartic
interactions, where the signature of noncommutativity appears in
-dependent terms. The implications of this approach, which avoids the
problems related to UV-IR mixing, are discussed from the perspective of the
Wilson renormalisation program. Finally, we remark about the generality of the
method, arguing that it may lead to phenomenologically relevant predictions,
when applied to realistic field theories.Comment: 1+11 pages, 6 figures; v2: references added, typos corrected,
conclusions unchange
Continuous Fuzzy Measurement of Energy for a Two-Level System
A continuous measurement of energy which is sharp (perfect) leads to the
quantum Zeno effect (freezing of the state). Only if the quantum measurement is
fuzzy, continuous monitoring gives a readout E(t) from which information about
the dynamical development of the state vector of the system may be obtained in
certain cases. This is studied in detail. Fuzziness is thereby introduced with
the help of restricted path integrals equivalent to non-Hermitian Hamiltonians.
For an otherwise undisturbed multilevel system it is shown that this
measurement represents a model of decoherence. If it lasts long enough, the
measurement readout discriminates between the energy levels and the von Neumann
state reduction is obtained. For a two-level system under resonance influence
(which undergoes in absence of measurement Rabi oscillations between the
levels) different regimes of measurement are specified depending on its
duration and fuzziness: 1) the Zeno regime where the measurement results in a
freezing of the transitions between the levels and 2) the Rabi regime when the
transitions maintain. It is shown that in the Rabi regime at the border to the
Zeno regime a correlation exists between the time dependent measurement readout
and the modified Rabi oscillations of the state of the measured system.
Possible realizations of continuous fuzzy measurements of energy are sketched.Comment: 29 pages in LATEX, 1 figure in EPS, to be published in Physical
Review
The numerical approach to quantum field theory in a non-commutative space
Numerical simulation is an important non-perturbative tool to study quantum
field theories defined in non-commutative spaces. In this contribution, a
selection of results from Monte Carlo calculations for non-commutative models
is presented, and their implications are reviewed. In addition, we also discuss
how related numerical techniques have been recently applied in computer
simulations of dimensionally reduced supersymmetric theories.Comment: 15 pages, 6 figures, invited talk presented at the Humboldt Kolleg
"Open Problems in Theoretical Physics: the Issue of Quantum Space-Time", to
appear in the proceedings of the Corfu Summer Institute 2015 "School and
Workshops on Elementary Particle Physics and Gravity" (Corfu, Greece, 1-27
September 2015
Towards Noncommutative Fuzzy QED
We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4.
We write down the effective action on fuzzy S**2 x S**2 and show the existence
of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We
also give a derivation of the beta function and comment on the limit of large
mass of the normal scalar fields. We also discuss topology change in this 4
fuzzy dimensions arising from the interaction of fields (matrices) with
spacetime through its noncommutativity.Comment: 33 page
A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences
Aggregation on bipolar scales
The paper addresses the problem of extending aggregation operators typically defined on to the symmetric interval , where the ``0'' value plays a particular role (neutral value). We distinguish the cases where aggregation operators are associative or not. In the former case, the ``0'' value may play the role of neutral or absorbant element, leading to pseudo-addition and pseudo-multiplication. We address also in this category the special case of minimum and maximum defined on some finite ordinal scale. In the latter case, we find that a general class of extended operators can be defined using an interpolation approach, supposing the value of the aggregation to be known for ternary vectors.bipolar scale; bi-capacity; aggregation
An empirical study of statistical properties of Choquet and Sugeno integrals
This paper investigates the statistical properties of the Choquet and Sugeno integrals, used as multiattribute models. The investigation is done on an empirical basis, and focuses on two topics: the distribution of the output of these integrals when the input is corrupted with noise, and the robustness of these models, when they are identified using some set of learning data through some learning procedure.Choquet integral; Sugeno integral; output distribution
Decomposition approaches to integration without a measure
Extending the idea of Even and Lehrer [3], we discuss a general approach to
integration based on a given decomposition system equipped with a weighting
function, and a decomposition of the integrated function. We distinguish two
type of decompositions: sub-decomposition based integrals (in economics linked
with optimization problems to maximize the possible profit) and
super-decomposition based integrals (linked with costs minimization). We
provide several examples (both theoretical and realistic) to stress that our
approach generalizes that of Even and Lehrer [3] and also covers problems of
linear programming and combinatorial optimization. Finally, we introduce some
new types of integrals related to optimization tasks.Comment: 15 page
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