Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine structure. We show that a simple unitary transformation leads directly to the familiar Breit-Fermi spin-spin and tensor interactions, which can be treated in degenerate first-order bound-state perturbation theory, thus simplifying analytic light-front QED calculations. To the order in momenta we need to consider, this transformation is equivalent to a Melosh rotation. We also study how the similarity transformation affects spin-orbit interactions.Comment: 17 pages, latex fil

Initial bound state studies in light-front QCD

We present the first numerical QCD bound state calculation based on a renormalization group-improved light-front Hamiltonian formalism. The QCD Hamiltonian is determined to second order in the coupling, and it includes two-body confining interactions. We make a momentum expansion, obtaining an equal-time-like Schrodinger equation. This is solved for quark-antiquark constituent states, and we obtain a set of self-consistent parameters by fitting B meson spectra.Comment: 38 pages, latex, 5 latex figures include

Quarkonia in Hamiltonian Light-Front QCD

A constituent parton picture of hadrons with logarithmic confinement naturally arises in weak coupling light-front QCD. Confinement provides a mass gap that allows the constituent picture to emerge. The effective renormalized Hamiltonian is computed to ${\cal O}(g^2)$, and used to study charmonium and bottomonium. Radial and angular excitations can be used to fix the coupling $\alpha$, the quark mass $M$, and the cutoff $\Lambda$. The resultant hyperfine structure is very close to experiment.Comment: 9 pages, 1 latex figure included in the text. Published version (much more reader-friendly); corrected error in self-energ

Nonperturbative renormalization in a scalar model within Light-Front Dynamics

Within the covariant formulation of Light-Front Dynamics, in a scalar model with the interaction Hamiltonian $H=-g\psi^{2}(x)\phi(x)$, we calculate nonperturbatively the renormalized state vector of a scalar "nucleon" in a truncated Fock space containing the $N$, $N\pi$ and $N\pi\pi$ sectors. The model gives a simple example of non-perturbative renormalization which is carried out numerically. Though the mass renormalization $\delta m^2$ diverges logarithmically with the cutoff $L$, the Fock components of the "physical" nucleon are stable when $L\to\infty$.Comment: 22 pages, 5 figure

Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization

Hamiltonian light-front field theory can be used to solve for hadron states in QCD. To this end, a method has been developed for systematic renormalization of Hamiltonian light-front field theories, with the hope of applying the method to QCD. It assumed massless particles, so its immediate application to QCD is limited to gluon states or states where quark masses can be neglected. This paper builds on the previous work by including particle masses non-perturbatively, which is necessary for a full treatment of QCD. We show that several subtle new issues are encountered when including masses non-perturbatively. The method with masses is algebraically and conceptually more difficult; however, we focus on how the methods differ. We demonstrate the method using massive phi^3 theory in 5+1 dimensions, which has important similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final published versio

Renormalized Effective QCD Hamiltonian: Gluonic Sector

Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.Comment: 25 pages, no figures, revte

Asymptotic Freedom and Bound States in Hamiltonian Dynamics

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.Comment: plain latex file, 15 pages, 6 latex figures 1 page each, 1 tabl

Systematic Renormalization in Hamiltonian Light-Front Field Theory

We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping any Fock sectors from the theory, and to regulate the Hamiltonian, we suppress the matrix elements of the Hamiltonian between free-particle Fock-space states that differ in free mass by more than a cutoff. The cutoff violates a number of physical principles of the theory, and thus the Hamiltonian is not just the canonical Hamiltonian with masses and couplings redefined by renormalization. Instead, the Hamiltonian must be allowed to contain all operators that are consistent with the unviolated physical principles of the theory. We show that if we require the Hamiltonian to produce cutoff-independent physical quantities and we require it to respect the unviolated physical principles of the theory, then its matrix elements are uniquely determined in terms of the fundamental parameters of the theory. This method is designed to be applied to QCD, but for simplicity, we illustrate our method by computing and analyzing second- and third-order matrix elements of the Hamiltonian in massless phi-cubed theory in six dimensions.Comment: 47 pages, 6 figures; improved referencing, minor presentation change

Interventions for drug-using offenders with co-occurring mental illness::A systematic review and economic appraisal

Background: Drug-using offenders with co-occurring mental health problems are common in the criminal justice system. A combination of drug use and mental health problems makes people more likely to be arrested for criminal involvement after release compared to offenders without a mental health problem. Previous research has evaluated interventions aimed broadly at those with a drug problem but rarely with drug use and mental health problems. This systematic review considers the effectiveness of interventions for drug-using offenders with co-occurring mental health problems. Methods: We searched 14 electronic bibliographic databases up to May 2014 and five Internet resources. The review included randomised controlled trials designed to reduce, eliminate, or prevent relapse of drug use and/or criminal activity. Data were reported on drug and crime outcomes, the identification of mental health problems, diagnoses and resource information using the Drummond checklist. The systematic review used standard methodological procedures as prescribed by the Cochrane collaboration. Results: Eight trials with 2058 participants met the inclusion criteria. These evaluated: case management (RR, 1.05, 95 % CI 0.90 to 1.22, 235 participants), motivational interviewing and cognitive skills, (MD-7.42, 95 % CI-0.20.12 to 5.28, 162 participants) and interpersonal psychotherapy (RR 0.67, 95 % CI 0.3 to 1.5, 38 participants). None of these trials reported significant reductions in self-report drug misuse or crime. Four trials evaluating differing therapeutic community models showed reductions in re-incarceration (RR 0.28, 95 % CI 0.13 to 0.63, 139 participants) but not re-arrest (RR 1.65, 95 % CI 0.83 to 3.28, 370 participants) or self-report drug use (RR 0.73, 95 % CI 0.53 to 1.01, 370 participants). Mental health problems were identified across the eight trials and 17 different diagnoses were described. Two trials reported some resource information suggesting a cost-beneficial saving when comparing therapeutic communities to a prison alternative. Conclusions: Overall, the studies showed a high degree of variation, warranting a degree of caution in the interpretation of the magnitude of effect and direction of benefit for treatment outcomes. Specifically, tailored interventions are required to assess the effectiveness of interventions for drug-using offenders with co-occurring mental health problems

Mental toughness and transitions to high school and to undergraduate study

Mental toughness can be conceptualised as a set of attributes that allow people to deal effectively with challenges, stressors and pressure. Recent work has suggested that it may be a valuable construct to consider within educational settings. The current studies explored the associations between mental toughness and educational transitions. Study 1 examined the relationships between mental toughness and concerns about moving to a new school in 105 children aged 12–13 years of age. The results revealed significant relationships between several aspects of mental toughness, but particularly confidence in abilities, and children’s concerns. Study 2 examined the relationships between mental toughness and adjustment to university in 200 undergraduate students at various stages of their course. The results revealed a role for several aspects of mental toughness; commitment, control of life, control of emotion, confidence in abilities and interpersonal confidence. The results are discussed in terms of implications for educational practice. It is suggested that measures of mental toughness could be used to identify individuals who may benefit from additional support during transition to a new school or to university, and that future research should explore the potential benefits of mental toughness training. © 2016 Informa UK Limited, trading as Taylor & Francis Group