Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry

The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on supersphere [14]. This paper is a generalization of this latter work to more general gauge groups

Quantum cosmology of 5D non-compactified Kaluza-Klein theory

We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l=constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the $l\simeq0$ constant hypersurface.Comment: 14 pages, LaTe

Operator identities in q-deformed Clifford analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied

Examples of q-regularization

An Introduction to Hopf algebras as a tool for the regularization of relavent quantities in quantum field theory is given. We deform algebraic spaces by introducing q as a regulator of a non-commutative and non-cocommutative Hopf algebra. Relevant quantities are finite provided q\neq 1 and diverge in the limit q\rightarrow 1. We discuss q-regularization on different q-deformed spaces for \lambda\phi^4 theory as example to illustrate the idea.Comment: 17 pages, LaTex, to be published in IJTP 1995.1

The N=1 superstring as a topological field theory

By "untwisting" the construction of Berkovits and Vafa, one can see that the N=1 superstring contains a topological twisted N=2 algebra, with central charge c^ = 2. We discuss to what extent the superstring is actually a topological theory.Comment: 8 Pages (LaTeX). TAUP-2155-9

q-Deforming Maps for Lie Group Covariant Heisenberg Algebras

We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.Comment: latex file, 4 pages. Contribution to the proceedings of the 5th Wigner Symposium. Slight modification

On the physical contents of q-deformed Minkowski spaces

Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.Comment: some changes mad

A review of maps in PhDs : is your map worth a 1000 words?

Maps are useful for providing location context and for graphically presenting spatial relationships. They are often used in PhD dissertations to show the location of a study area or to present scientific results. These maps have to tell their story without the PhD candidate being present. We searched for maps in 575 PhD dissertations, and reviewed 192 maps in 65 of these: 38% were created by PhD candidates, 48% were inserted and 14% were adapted from other sources. Maps prepared by PhD candidates had more design shortcomings than other maps. Nevertheless, the number of problems with maps from other sources suggests that guidelines for including them in a dissertation could be useful. Our results suggest that PhD candidates use GIS software to design maps, but that there is room for improvement to guide users towards appropriate design choices. The results will help to plan support services for PhD candidates at universities.https://www.tandfonline.com/loi/ycaj20hj2023Geography, Geoinformatics and Meteorolog

Nonpointlike Particles in Harmonic Oscillators

Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation relations induce a finite lower bound to spatial localisation. Here, we perturbatively calculate the corrections to the energy levels of an in this sense nonpointlike particle in isotropic harmonic oscillators. Apart from a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio

Operator Formalism on General Algebraic Curves

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems is developed. The physical states are expressed by means of creation and annihilation operators as in the complex plane and the correlation functions are evaluated starting from simple normal ordering rules. The Hilbert space of the theory exhibits an interesting internal structure, being splitted into $n$ ($n$ is the number of branches of the curve) independent Hilbert spaces. Exploiting the operator formalism a large collection of explicit formulas of string theory is derived.Comment: 34 pages of plain TeX + harvmac, With respect to the first version some new references have been added and a statement in the Introduction has been change