Coarse-Graining and Renormalization Group in the Einstein Universe

The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes is constructed in a nonflat background and explicitly computed within the loop-expansion approximation for an Einstein universe. The curvature turns out to be dominant in setting the crossover scale from a double-peak and a symmetric distribution of the block variables. The evolution of all the coupling constants generated by the blocking procedure is examined: the renormalized trajectories agree with the standard perturbative results for the relevant vertices near the ultraviolet fixed point, but new effective interactions between gravity and matter are present. The flow of the conformal coupling constant is therefore analyzed in the improved scheme and the infrared fixed point is reached for arbitrary values of the renormalized parameters.Comment: 18 pages, REVTex, two uuencoded figures. (to appear in Phys. Rev. D15, July) Transmission errors have been correcte

Multiple self-reported concussions are more prevalent in athletes with ADHD and learning disability

Objective: We evaluated how attention deficit-hyperactivity disorder (ADHD) and learning disability (LD) are associated with concussion history and performance on standard concussion assessment measures. Based on previous reports that developmental disorders are associated with increased injury proneness and poorer cognitive performance, we anticipated that ADHD and LD would be associated with increased history of concussion and poorer baseline performance on assessment measures. Design: Cross-sectional study. Setting: Clinical research center. Participants: The study sample aggregated data from two separate projects: the National Collegiate Athletic Association Concussion Study and Project Sideline. Interventions: We analyzed preseason baseline data from 8056 high school and collegiate athletes (predominantly male football players) enrolled in prior studies of sport-related concussion. Main Outcome Measures: Measures included demographic/health history, symptoms, and cognitive performance. Results: Attention deficit-hyperactivity disorder and LD were associated with 2.93 and 2.08 times the prevalence, respectively, of 3+ historical concussions (for comorbid ADHD/LD the prevalence ratio was 3.38). In players without histories of concussion, individuals with ADHD reported more baseline symptoms, and ADHD and LD were associated with poorer performance on baseline cognitive tests. Interactive effects were present between ADHD/LD status and concussion history for self-reported symptoms. Conclusions: Neurodevelopmental disorders and concussion history should be jointly considered in evaluating concussed players. Clinical Relevance: Clinical judgments of self-reported symptoms and cognitive performance should be adjusted based on athletes' individual preinjury baselines or comparison with appropriate normative samples

Thermodynamic Gravity and the Schrodinger Equation

We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in the Universe as a 'gravitationally entangled' statistical ensemble and apply the approach of classical statistical mechanics to it. It is shown that both the Schrodinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy

Infrared problem for the Nelson model on static space-times

We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. A physical example is obtained by quantizing the Klein-Gordon equation on a static space-time coupled with a non-relativistic particle. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass tends to 0 at infinity

Critical Dynamics of Magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole--dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three--dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.Comment: Review article (154 pages, figures included

Improved perturbation theory in the vortex liquids state of type II superconductors

We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is $a_{T}=-3$ in 2D and $a_{T}=-5$ in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.Comment: 24 pages, 9 figure

Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2$ and Euler number $\chi = 0$ in contrast to the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black holes as having an inner boundary, we conclude that the entropy of {\sl all} extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the relevance of this to the vanishing of quantum corrections and the idea that the functional integral for extreme holes gives a Witten Index. We have studied also the topology of ``moduli space'' of multi black holes. The quantum mechanics on black hole moduli spaces is expected to be supersymmetric despite the fact that they are not HyperK\"ahler since the corresponding geometry has torsion unlike the BPS monopole case. Finally, we describe the possibility of extreme black hole fission for states with an energy gap. The energy released, as a proportion of the initial rest mass, during the decay of an electro-magnetic black hole is 300 times greater than that released by the fission of an ${}^{235} U$ nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New sections include discussion of the Witten index, topology of the moduli space, black hole sigma model, and black hole fission with huge energy releas

Spontaneous CP Violation in Non-Minimal Supersymmetric Models

We study the possibilities of spontaneous CP violation in the Next-to-Minimal Supersymmetric Standard Model with an extra singlet tadpole term in the scalar potential. We calculate the Higgs boson masses and couplings with radiative corrections including dominant two loop terms. We show that it is possible to satisfy the LEP constraints on the Higgs boson spectrum with non-trivial spontaneous CP violating phases. We also show that these phases could account for the observed value of epsilonK.Comment: 21 pages, 7 Figures in Encapsulated Postscrip