FFZ realization of the deformed super Virasoro algebra - Chaichian-Presnajder type

The q-deformed super Virasoro algebra proposed by Chaichian and Presnajder is examined. Presented is the realizations by the FFZ algebra (the magnetic translation algebra) defined on a two-dimensional lattice with a supersymmetric Hamiltonian.Comment: Latex 9 pages, a couple of short comments are adde

Integral representations of thermodynamic 1PI Green functions in the world-line formalism

The issue discussed is a thermodynamic version of the Bern-Kosower master amplitude formula, which contains all necessary one-loop Feynman diagrams. It is demonstrated how the master amplitude at finite values of temperature and chemical potential can be formulated within the framework of the world-line formalism. In particular we present an elegant method how to introduce a chemical potential for a loop in the master formula. Various useful integral formulae for the master amplitude are then obtained. The non-analytic property of the master formula is also derived in the zero temperature limit with the value of chemical potential kept finite.Comment: 1+30 pages, improved presentatio

World-line Green functions with momentum and source conservations

Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the momentum conservation law of a certain nontrivial form, and transforms ambiguous Green functions into the uniquely defined Green functions. We also argue reparametrizations of the Green functions defined on differently parameterized world-line diagrams.Comment: 20(+1) pages, one pictex figur

On Bogoliubov Transformation of Scalar Wave Functions in De Sitter Space

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables.Comment: 16 pages, OU-HET 202, LMU-TPW 94-1

Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories

One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete agreement of the result with Seiberg-Witten limit of string worldsheet computation and standard Feynman diagrammatics. We prove that, at low-energy and large noncommutativity limit, nonplanar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators.Comment: 26 pages, Latex, 4 eps figures, v2. typos corrected, v3. combinatorics correcte

Deformation of Super Virasoro Algebra in Noncommutative Quantum Superspace

We present a twisted commutator deformation for $N=1,2$ super Virasoro algebras based on $GL_q(1,1)$ covariant noncommutative superspace.Comment: 10 pages, Late