Nonlocal regularization of abelian models with spontaneous symmetry breaking

We demonstrate how nonlocal regularization is applied to gauge invariant models with spontaneous symmetry breaking. Motivated by the ability to find a nonlocal BRST invariance that leads to the decoupling of longitudinal gauge bosons from physical amplitudes, we show that the original formulation of the method leads to a nontrivial relationship between the nonlocal form factors that can appear in the model.Comment: 11 pages, uses amsart. To appear in Mod. Phys. Lett

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Support varieties for selfinjective algebras

Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true

Modular classes of skew algebroid relations

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.Comment: 20 page

Ultraviolet Complete Electroweak Model Without a Higgs Particle

An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The $W$ and $Z$ masses are compatible with a symmetry breaking $SU(2)_L\times U(1)_Y \rightarrow U(1)_{\rm em}$, which retains a massless photon. The vertex couplings possess an energy scale $\Lambda_W > 1$ TeV predicting scattering amplitudes that can be tested at the LHC.Comment: 19 pages, no figures, LaTex file. Equation and text corrected. Reference added. Results remain the same. Final version published in European Physics Journal Plus, 126 (2011

Multiplicative slices, relativistic Toda and shifted quantum affine algebras

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.Comment: 125 pages. v2: references updated; in section 11 the third local Lax matrix is introduced. v3: references updated. v4=v5: 131 pages, minor corrections, table of contents added, Conjecture 10.25 is now replaced by Theorem 10.25 (whose proof is based on the shuffle approach and is presented in a new Appendix). v6: Final version as published, references updated, footnote 4 adde

Regularization as quantization in reducible representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a classical current. The scheme implies a modified but very physically looking Hamiltonian. We solve Heisenberg equations of motion and compute photon statistics. Poisson statistics naturally occurs and no infrared divergence is found even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincar\'e covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to R\'enyi's $\alpha$. It is shown that the ``Shannon limit" $\alpha\to 1$ plays here a role of correspondence principle with the standard regularized formalism.Comment: minor extensions, version submitted for publicatio

Analyzing collaborative learning processes automatically

In this article we describe the emerging area of text classification research focused on the problem of collaborative learning process analysis both from a broad perspective and more specifically in terms of a publicly available tool set called TagHelper tools. Analyzing the variety of pedagogically valuable facets of learners’ interactions is a time consuming and effortful process. Improving automated analyses of such highly valued processes of collaborative learning by adapting and applying recent text classification technologies would make it a less arduous task to obtain insights from corpus data. This endeavor also holds the potential for enabling substantially improved on-line instruction both by providing teachers and facilitators with reports about the groups they are moderating and by triggering context sensitive collaborative learning support on an as-needed basis. In this article, we report on an interdisciplinary research project, which has been investigating the effectiveness of applying text classification technology to a large CSCL corpus that has been analyzed by human coders using a theory-based multidimensional coding scheme. We report promising results and include an in-depth discussion of important issues such as reliability, validity, and efficiency that should be considered when deciding on the appropriateness of adopting a new technology such as TagHelper tools. One major technical contribution of this work is a demonstration that an important piece of the work towards making text classification technology effective for this purpose is designing and building linguistic pattern detectors, otherwise known as features, that can be extracted reliably from texts and that have high predictive power for the categories of discourse actions that the CSCL community is interested in