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

Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

Action research in physical education: focusing beyond myself through cooperative learning

This paper reports on the pedagogical changes that I experienced as a teacher engaged in an action research project in which I designed and implemented an indirect, developmentally appropriate and child‐centred approach to my teaching. There have been repeated calls to expunge – or at least rationalise – the use of traditional, teacher‐led practice in physical education. Yet despite the advocacy of many leading academics there is little evidence that such a change of approach is occurring. In my role as teacher‐as‐researcher I sought to implement a new pedagogical approach, in the form of cooperative learning, and bring about a positive change in the form of enhanced pupil learning. Data collection included a reflective journal, post‐teaching reflective analysis, pupil questionnaires, student interviews, document analysis, and non‐participant observations. The research team analysed the data using inductive analysis and constant comparison. Six themes emerged from the data: teaching and learning, reflections on cooperation, performance, time, teacher change, and social interaction. The paper argues that cooperative learning allowed me to place social and academic learning goals on an even footing, which in turn placed a focus on pupils’ understanding and improvement of skills in athletics alongside their interpersonal development

Final state interaction phase in B decays

From an estimate of the meson-meson inelastic scatterin at 5 GeV it is concluded that a typical strong phase in B decays to two mesons is of order of 20 degrees. For a particular final state an estimate of the phase depends on whether that state is more or less probable as a final state compared to those states to which it is connected by the strong interaction S matrix.Comment: 10 pages in RevTex with 1 eps figur

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

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.Comment: 17 pages(LaTeX REVTeX), 1 figure appended (PostScript), Technical Report of ISSP A-274

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

Energy level statistics for models of coupled single-mode Bose--Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.Comment: 5 pages, 4 figures, revte

Distribution of the Riemann zeros represented by the Fermi gas

The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.Comment: 7 page