951,235 research outputs found
Introduction to linear logic and ludics, part II
This paper is the second part of an introduction to linear logic and ludics,
both due to Girard. It is devoted to proof nets, in the limited, yet central,
framework of multiplicative linear logic and to ludics, which has been recently
developped in an aim of further unveiling the fundamental interactive nature of
computation and logic. We hope to offer a few computer science insights into
this new theory
Computational Tools for Cohomology of Toric Varieties
In this review, novel non-standard techniques for the computation of
cohomology classes on toric varieties are summarized. After an introduction of
the basic definitions and properties of toric geometry, we discuss a specific
computational algorithm for the determination of the dimension of line-bundle
valued cohomology groups on toric varieties. Applications to the computation of
chiral massless matter spectra in string compactifications are discussed and,
using the software package cohomCalg, its utility is highlighted on a new
target space dual pair of (0,2) heterotic string models.Comment: 17 pages, 4 tables; prepared for the special issue "Computational
Algebraic Geometry in String and Gauge Theory" of Advances in High Energy
Physics, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Covariance approach to the free photon field
We introduce photon theory following the same principles as for introduction
of the quantum theory of a single particle, using a C*-algebraic approach based
on covariance systems. The basic symmetries are additivity of the fields and
additivity of test functions. We write down in explicit form a state of this
covariance system. It turns out to reproduce the traditional Fock
representation of the free photon field, with a Lorentz invariant vacuum.
Properties of smeared-out photons are discussed.Comment: Latex, 24 pages, to appear in: "Probing the structure of Quantum
Mechanics: nonlinearity, nonlocality, computation and axiomatics", eds. D.
Aerts, M. Czachor, and T. Durt (World Scientific, 2002
The Lifting Properties of A-Homotopy Theory
In classical homotopy theory, two spaces are homotopy equivalent if one space
can be continuously deformed into the other. This theory, however, does not
respect the discrete nature of graphs. For this reason, a discrete homotopy
theory that recognizes the difference between the vertices and edges of a graph
was invented, called A-homotopy theory [1-5]. In classical homotopy theory,
covering spaces and lifting properties are often used to compute the
fundamental group of the circle. In this paper, we develop the lifting
properties for A-homotopy theory. Using a covering graph and these lifting
properties, we compute the fundamental group of the 5-cycle , giving an
alternate approach to [4].Comment: 27 pages, 3 figures, updated version. Minor changes to the
introduction and clarification that the computation of the fundamental group
of the 5-cycle originally appeared in [4]. Title changed from "Computing
A-Homotopy Groups Using Coverings and Lifting Properties" to "The Lifting
Properties of A-Homotopy Theory
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