7,658 research outputs found
On Finite 4D Quantum Field Theory in Non-Commutative Geometry
The truncated 4-dimensional sphere and the action of the
self-interacting scalar field on it are constructed. The path integral
quantization is performed while simultaneously keeping the SO(5) symmetry and
the finite number of degrees of freedom. The usual field theory UV-divergences
are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove
Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator
It is shown that the local axial anomaly in dimensions emerges naturally
if one postulates an underlying noncommutative fuzzy structure of spacetime .
In particular the Dirac-Ginsparg-Wilson relation on is shown to
contain an edge effect which corresponds precisely to the ``fuzzy''
axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant
expansion of the quark propagator in the form where
is the lattice spacing on , is
the covariant noncommutative chirality and is an effective
Dirac operator which has essentially the same IR spectrum as
but differes from it on the UV modes. Most remarkably is the fact that both
operators share the same limit and thus the above covariant expansion is not
available in the continuum theory . The first bit in this expansion
although it vanishes as it stands in the continuum
limit, its contribution to the anomaly is exactly the canonical theta term. The
contribution of the propagator is on the other hand
equal to the toplogical Chern-Simons action which in two dimensions vanishes
identically .Comment: 26 pages, latex fil
Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry
The non commutative geometry is a possible framework to regularize Quantum
Field Theory in a nonperturbative way. This idea is an extension of the lattice
approximation by non commutativity that allows to preserve symmetries. The
supersymmetric version is also studied and more precisely in the case of the
Schwinger model on supersphere [14]. This paper is a generalization of this
latter work to more general gauge groups
A New Noncommutative Product on the Fuzzy Two-Sphere Corresponding to the Unitary Representation of SU(2) and the Seiberg-Witten Map
We obtain a new explicit expression for the noncommutative (star) product on
the fuzzy two-sphere which yields a unitary representation. This is done by
constructing a star product, , for an arbitrary representation
of SU(2) which depends on a continuous parameter and searching for
the values of which give unitary representations. We will find two
series of values: and
, where j is the spin of the representation
of SU(2). At the new star product
has poles. To avoid the singularity the functions on the sphere must be
spherical harmonics of order and then reduces
to the star product obtained by Preusnajder. The star product at
, to be denoted by , is new. In this case the
functions on the fuzzy sphere do not need to be spherical harmonics of order
. Because in this case there is no cutoff on the order of
spherical harmonics, the degrees of freedom of the gauge fields on the fuzzy
sphere coincide with those on the commutative sphere. Therefore, although the
field theory on the fuzzy sphere is a system with finite degrees of freedom, we
can expect the existence of the Seiberg-Witten map between the noncommutative
and commutative descriptions of the gauge theory on the sphere. We will derive
the first few terms of the Seiberg-Witten map for the U(1) gauge theory on the
fuzzy sphere by using power expansion around the commutative point .Comment: 15 pages, typos corrected, references added, a note adde
The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized
at the one-loop level by multiplicative dimensional renormalization of the
coupling constant and fields of the theory. We compute the beta function of the
theory and conclude that the theory is asymptotically free. We also show that
the Weyl-Moyal matrix defining the deformed product over the space of functions
on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and
the divergent contributions corrected accordingly. As a result the model
turns out to be asymptotically fre
A compact and robust diode laser system for atom interferometry on a sounding rocket
We present a diode laser system optimized for laser cooling and atom
interferometry with ultra-cold rubidium atoms aboard sounding rockets as an
important milestone towards space-borne quantum sensors. Design, assembly and
qualification of the system, combing micro-integrated distributed feedback
(DFB) diode laser modules and free space optical bench technology is presented
in the context of the MAIUS (Matter-wave Interferometry in Microgravity)
mission.
This laser system, with a volume of 21 liters and total mass of 27 kg, passed
all qualification tests for operation on sounding rockets and is currently used
in the integrated MAIUS flight system producing Bose-Einstein condensates and
performing atom interferometry based on Bragg diffraction. The MAIUS payload is
being prepared for launch in fall 2016.
We further report on a reference laser system, comprising a rubidium
stabilized DFB laser, which was operated successfully on the TEXUS 51 mission
in April 2015. The system demonstrated a high level of technological maturity
by remaining frequency stabilized throughout the mission including the rocket's
boost phase
Causal Consistency of Structural Equation Models
Complex systems can be modelled at various levels of detail. Ideally, causal
models of the same system should be consistent with one another in the sense
that they agree in their predictions of the effects of interventions. We
formalise this notion of consistency in the case of Structural Equation Models
(SEMs) by introducing exact transformations between SEMs. This provides a
general language to consider, for instance, the different levels of description
in the following three scenarios: (a) models with large numbers of variables
versus models in which the `irrelevant' or unobservable variables have been
marginalised out; (b) micro-level models versus macro-level models in which the
macro-variables are aggregate features of the micro-variables; (c) dynamical
time series models versus models of their stationary behaviour. Our analysis
stresses the importance of well specified interventions in the causal modelling
process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted
manuscrip
Industrial practitioners' mental models of adversarial machine learning
Although machine learning is widely used in practice, little is known about practitioners' understanding of potential security challenges. In this work, we close this substantial gap and contribute a qualitative study focusing on developers' mental models of the machine learning pipeline and potentially vulnerable components. Similar studies have helped in other security fields to discover root causes or improve risk communication. Our study reveals two facets of practitioners' mental models of machine learning security. Firstly, practitioners often confuse machine learning security with threats and defences that are not directly related to machine learning. Secondly, in contrast to most academic research, our participants perceive security of machine learning as not solely related to individual models, but rather in the context of entire workflows that consist of multiple components. Jointly with our additional findings, these two facets provide a foundation to substantiate mental models for machine learning security and have implications for the integration of adversarial machine learning into corporate workflows, decreasing practitioners' reported uncertainty, and appropriate regulatory frameworks for machine learning security
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