9,489 research outputs found
Experimenting with Strategic Experimentation: Risk Taking, Neighborhood Size and Network Structure
This paper investigates the effects of neighborhood size and network structure on strategic experimentation. We analyze a multi-arm bandit game with one safe and two risky alternatives. In this setting, risk taking produces a learning externality and an opportunity for free riding. We conduct a laboratory experiment to investigate whether group size and the network structure affect risk taking. We find that group size has an effect on risk taking that is qualitatively in line with equilibrium predictions. Introducing an asymmetry among agents in the same network with respect to neighborhood size leads to substantial deviations from equilibrium play. Findings suggests that subjects react to changes in their direct neighborhood but fail to play a best-response to their position within the network.strategic experimentation, experiment, bandit game, risk taking
Noncommutative QFT and Renormalization
Field theories on deformed spaces suffer from the IR/UV mixing and
renormalization is generically spoiled. In work with R. Wulkenhaar, one of us
realized a way to cure this disease by adding one more marginal operator. We
review these ideas, show the application to models and use the heat
kernel expansion methods for a scalar field theory coupled to an external gauge
field on a -deformed space and derive noncommutative gauge field
actions.Comment: To appear in the proceedings of the Workshop "Noncommutative Geometry
in Field and String Theory", Corfu, 2005 (Greece
Functional Renormalization of Noncommutative Scalar Field Theory
In this paper we apply the Functional Renormalization Group Equation (FRGE)
to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar.
We derive the flow equation in the matrix representation and discuss the theory
space for the self-dual model. The features introduced by the external
dimensionful scale provided by the non-commutativity parameter, originally
pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a
technical assumption, but without resorting to any truncation, it is then shown
that the theory is asymptotically safe for suitably small values of the
coupling, recovering the result of \cite{disertori:2007}. Finally, we
show how the FRGE can be easily used to compute the one loop beta-functions of
the duality covariant model.Comment: 38 pages, no figures, LaTe
Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions
The integrability of -gravity with torsion in two dimensions is traced
to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian
phase space. It may be interpreted as a quadratically deformed
-algebra with the deformation consisting of the Casimir operators of
the undeformed algebra. The locally conserved quantity encountered in the
explicit solution is identified as an element of the centre of this algebra.
Specific contractions of the algebra are related to specific limits of the
explicit solutions of this model.Comment: 17 pages, TUW-92-04 (LaTeX
Geometry of the Grosse-Wulkenhaar Model
We define a two-dimensional noncommutative space as a limit of finite-matrix
spaces which have space-time dimension three. We show that on such space the
Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the
action for the scalar field coupled to the curvature. We also discuss a natural
generalization to four dimensions.Comment: 16 pages, version accepted in JHE
Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics
A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Krein’s spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift function, the Witten index, and the anomaly. In particular, a complete treatment of the two‐dimensional magnetic field problem is given, without assuming that the magnetic flux is quantized
Induced Gauge Theory on a Noncommutative Space
We discuss the calculation of the 1-loop effective action on four
dimensional, canonically deformed Euclidean space. The theory under
consideration is a scalar model with an additional oscillator
potential. This model is known to be re normalisable. Furthermore, we couple an
exterior gauge field to the scalar field and extract the dynamics for the gauge
field from the divergent terms of the 1-loop effective action using a matrix
basis. This results in proposing an action for noncommutative gauge theory,
which is a candidate for a renormalisable model.Comment: 8 page
On the biparametric quantum deformation of GL(2) x GL(1)
We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit
its cross-product structure. We derive explictly the associated dual algebra,
i.e., the quantised universal enveloping algebra employing the R-matrix
procedure. This facilitates construction of a bicovariant differential calculus
which is also shown to have a cross-product structure. Finally, a Jordanian
analogue of the deformation is presented as a cross-product algebra.Comment: 16 pages LaTeX, published in JM
Graded Differential Geometry of Graded Matrix Algebras
We study the graded derivation-based noncommutative differential geometry of
the -graded algebra of complex -matrices
with the ``usual block matrix grading'' (for ). Beside the
(infinite-dimensional) algebra of graded forms the graded Cartan calculus,
graded symplectic structure, graded vector bundles, graded connections and
curvature are introduced and investigated. In particular we prove the
universality of the graded derivation-based first-order differential calculus
and show, that is a ``noncommutative graded manifold'' in a
stricter sense: There is a natural body map and the cohomologies of and its body coincide (as in the case of ordinary graded manifolds).Comment: 21 pages, LATE
Spectral noncommutative geometry and quantization: a simple example
We explore the relation between noncommutative geometry, in the spectral
triple formulation, and quantum mechanics. To this aim, we consider a dynamical
theory of a noncommutative geometry defined by a spectral triple, and study its
quantization. In particular, we consider a simple model based on a finite
dimensional spectral triple (A, H, D), which mimics certain aspects of the
spectral formulation of general relativity. We find the physical phase space,
which is the space of the onshell Dirac operators compatible with A and H. We
define a natural symplectic structure over this phase space and construct the
corresponding quantum theory using a covariant canonical quantization approach.
We show that the Connes distance between certain two states over the algebra A
(two ``spacetime points''), which is an arbitrary positive number in the
classical noncommutative geometry, turns out to be discrete in the quantum
theory, and we compute its spectrum. The quantum states of the noncommutative
geometry form a Hilbert space K. D is promoted to an operator *D on the direct
product *H of H and K. The triple (A, *H, *D) can be viewed as the quantization
of the family of the triples (A, H, D).Comment: 7 pages, no figure
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