Background independent exact renormalization group for conformally reduced gravity

Within the conformally reduced gravity model, where the metric is parametrised by a function $f(\phi)$ of the conformal factor $\phi$, we keep dependence on both the background and fluctuation fields, to local potential approximation and $\mathcal{O}(\partial^2)$ 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 $k$ is inherently background dependent, which we show in general forbids the existence of RG fixed points with respect to $k$. 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, $\hat k$. 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 $f$. In general $f(\phi)$ is forced to be scale dependent and needs to be renormalised, but if this is avoided then $k$-fixed points are allowed and furthermore they coincide with $\hat k$-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

Correlation Widths in Quantum--Chaotic Scattering

An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the "transmission coefficient" in channel c and where the sum runs over all channels) provides a very good approximation to Gamma_{corr} even when the number of channels is small. That same conclusion applies also to the cross-section correlation function

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