6,621 research outputs found
Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization
We introduce normal coordinates on the infinite dimensional group
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on . For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
-primitiveness, which is shown to be equivalent to the one already in the
literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy
Microlensing of the broad-line region in the quadruply imaged quasar HE0435-1223
Using infrared spectra of the z = 1.693 quadruply lensed quasar HE0435-1223
acquired in 2009 with the spectrograph SINFONI at the ESO Very Large Telescope,
we have detected a clear microlensing effect in images A and D. While
microlensing affects the blue and red wings of the H{\alpha} line profile in
image D very differently, it de-magnifies the line core in image A. The
combination of these different effects sets constraints on the line-emitting
region; these constraints suggest that a rotating ring is at the origin of the
H{\alpha} line. Visible spectra obtained in 2004 and 2012 indicate that the
MgII line profile is microlensed in the same way as the H{\alpha} line. Our
results therefore favour flattened geometries for the low-ionization
line-emitting region, for example, a Keplerian disk. Biconical models cannot be
ruled out but require more fine-tuning. Flux ratios between the different
images are also derived and confirm flux anomalies with respect to estimates
from lens models with smooth mass distributions.Comment: 6 pages, 4 figures, 3 tables, accepted by A&A on 10 April 201
Real sector of the nonminimally coupled scalar field to self-dual gravity
A scalar field nonminimally coupled to gravity is studied in the canonical
framework, using self-dual variables. The corresponding constraints are first
class and polynomial. To identify the real sector of the theory, reality
conditions are implemented as second class constraints, leading to three real
configurational degrees of freedom per space point. Nevertheless, this
realization makes non-polynomial some of the constraints. The original complex
symplectic structure reduces to the expected real one, by using the appropriate
Dirac brackets. For the sake of preserving the simplicity of the constraints,
an alternative method preventing the use of Dirac brackets, is discussed. It
consists of converting all second class constraints into first class by adding
extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure
The effect of heat treatments on the constituent materials of a nuclear reactor pressure vessel in hydrogen environment
AbstractA nuclear reactor pressure vessel (NRPV) wall is formed by two layer of different materials: an inner layer of stainless steel (cladding material) and an outer layer of low carbon steel (base material) which is highly susceptible to corrosion related phenomena. A reduction of the mechanical properties of both materials forming the wall would appear due to the action of the harsh environment causing hydrogen embrittlement (HE) related phenomena. As a result of the manufacturing process, residual stresses and strains appear in the NRPV wall, thereby influencing the main stage in HE: hydrogen diffusion. A common engineering practice for reducing such states is to apply a tempering heat treatment. In this paper, a numerical analysis is carried out for revealing the influence of the heat treatment parameters (tempering temperature and tempering time) on the HE of a commonly used NRPV. To achieve this goal, a numerical model of hydrogen diffusion assisted by stress and strain was used considering diverse residual stress-strain states after tempering. This way, the obtained hydrogen accumulation during operation time of the NRPV provides insight into the better tempering conditions from the structural integrity point of view
The scalar sector in the Myers-Pospelov model
We construct a perturbative expansion of the scalar sector in the
Myers-Pospelov model, up to second order in the Lorentz violating parameter and
taking into account its higher-order time derivative character. This expansion
allows us to construct an hermitian positive-definite Hamiltonian which
provides a correct basis for quantization. Demanding that the modified normal
frequencies remain real requires the introduction of an upper bound in the
magnitude |k| of the momentum, which is a manifestation of the effective
character of the model. The free scalar propagator, including the corresponding
modified dispersion relations, is also calculated to the given order, thus
providing the starting point to consider radiative corrections when
interactions are introduced.Comment: Published in AIP Conf.Proc.977:214-223,200
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