14,602 research outputs found
Background independent exact renormalization group for conformally reduced gravity
Within the conformally reduced gravity model, where the metric is
parametrised by a function of the conformal factor , we keep
dependence on both the background and fluctuation fields, to local potential
approximation and respectively, making no other
approximation. Explicit appearances of the background metric are then dictated
by realising a remnant diffeomorphism invariance. The standard non-perturbative
Renormalization Group (RG) scale is inherently background dependent, which
we show in general forbids the existence of RG fixed points with respect to
. By utilising transformations that follow from combining the flow equations
with the modified split Ward identity, we uncover a unique background
independent notion of RG scale, . The corresponding RG flow equations
are then not only explicitly background independent along the entire RG flow
but also explicitly independent of the form of . In general is
forced to be scale dependent and needs to be renormalised, but if this is
avoided then -fixed points are allowed and furthermore they coincide with
-fixed points.Comment: 53 pages, broken reference correcte
Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton’s constant and or the cosmological constant can be considered inessential. We then apply these ideas to the Local Potential Approximation and approximations of a similar spirit such as the f (R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a ‘vacuum’ solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f (R) flow equations
Asymptotic safety in the f(R) approximation
In the asymptotic safety programme for quantum gravity, it is important to go
beyond polynomial truncations. Three such approximations have been derived
where the restriction is only to a general function f(R) of the curvature R>0.
We confront these with the requirement that a fixed point solution be smooth
and exist for all non-negative R. Singularities induced by cutoff choices force
the earlier versions to have no such solutions. However, we show that the most
recent version has a number of lines of fixed points, each supporting a
continuous spectrum of eigen-perturbations. We uncover and analyse the first
five such lines. Sensible fixed point behaviour may be achieved if one
consistently incorporates geometry/topology change. As an exploratory example,
we analyse the equations analytically continued to R<0, however we now find
only partial solutions.We show how these results are always consistent with,
and to some extent can be predicted from, a straightforward analysis of the
constraints inherent in the equations.Comment: Latex, 66 pages, published version, typos correcte
Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited
The fluctuations exhibited by the cross-sections generated in a
compound-nucleus reaction or, more generally, in a quantum-chaotic scattering
process, when varying the excitation energy or another external parameter, are
characterized by the width Gamma_corr of the cross-section correlation
function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a
method for its determination by simply counting the number of maxima featured
by the cross sections as function of the parameter under consideration. They,
actually, stated that the product of the average number of maxima per unit
energy range and Gamma_corr is constant in the Ercison region of strongly
overlapping resonances. We use the analogy between the scattering formalism for
compound-nucleus reactions and for microwave resonators to test this method
experimentally with unprecedented accuracy using large data sets and propose an
analytical description for the regions of isolated and overlapping resonances
Cross-Section Fluctuations in Chaotic Scattering
For the theoretical prediction of cross-section fluctuations in chaotic
scattering, the cross-section autocorrelation function is needed. That function
is not known analytically. Using experimental data and numerical simulations,
we show that an analytical approximation to the cross-section autocorrelation
function can be obtained with the help of expressions first derived by Davis
and Boose. Given the values of the average S-matrix elements and the mean level
density of the scattering system, one can then reliably predict cross-section
fluctuations
The local potential approximation in the background field formalism
Working within the familiar local potential approximation, and concentrating
on the example of a single scalar field in three dimensions, we show that the
commonly used approximation method of identifying the total and background
fields, leads to pathologies in the resulting fixed point structure and the
associated spaces of eigenoperators. We then show how a consistent treatment of
the background field through the corresponding modified shift Ward identity,
can cure these pathologies, restoring universality of physical quantities with
respect to the choice of dependence on the background field, even within the
local potential approximation. Along the way we point out similarities to what
has been previously found in the f(R) approximation in asymptotic safety for
gravity.Comment: 40 pages, version accepted by JHE
Sociocultural Risk Factors for Elevated Perceived Stress among African American Smokers
Introduction: African Americans experience unique stressors that may inhibit smoking cessation and enhance relapse rates. Few studies, however, have focused on risk factors for perceived stress among treatment seekers. Because African Americans are less likely to quit compared to the larger community, understanding factors associated with perceived stress among smokers has the potential to improve intervention outcomes. This study examined psychosocial and cultural correlates of stress in a sample of African American participants in a randomized controlled trial.
Methods: At baseline, participants reported demographic factors and completed assessments of smoking history, alcohol use, friend and household smoking, weight concerns, acculturation, depressive symptoms, and perceived stress (N = 325). Bivariate associations were examined, followed by multiple regression analyses to test independent relationships. The sample was comprised of mostly middle-aged males, with at least a high school education, who were single, and reported low household income. Participants were moderately nicotine dependent and smoked 18 cigarettes per day for 26 years.
Results: Perceived stress was inversely associated with age (r = -.16, p = .004), education (r = -.11, p = .04), household income (r = -.11, p = .047), and positively associated with being male (r = .13, p = .02). Stress perceptions were positively related to cigarettes per day (r = .11, p = .049), nicotine dependence (r = .20, p = .001), drinking frequency (r = .15, p = .008), drinking intensity (r = .14, p=.02), and inversely related to smoking duration (r = -.12, p = .03). We found positive associations between perceived stress and household smokers (r = .18, p = .004), and friends who smoke (r = .15, p = .01).
Perceived stress was also positively associated with post-cessation weight concern (r = .14, p = .01), a traditional African American cultural orientation; r = .12, p = .04), and depressive symptoms (r = .65, p
Conclusion: These findings have important intervention implications. Many of the risk factors for distress among African American smokers are modifiable. Interventions should prioritize addressing depression, household smoking environment, and stress among younger smokers, in addition to managing other stress-enhancing concerns like alcohol use
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