JUNIPER PUBLISHERS-Biostatistics and Biometrics Open Access Journal
On Multidisciplinary Potential Applications of Gauge Theories
Authored by Jean-Pierre Magnot*
We review how gauge theories, initial
introduced for classical mechanics and quantum led theory, seem to apply to
many fields of research such as information theory, computer science, economy,
biology. This non-exhaustive list raises natural question on future
developments of this theory. Basically, the mathematical structure of groups is
among the best adapted for describing transformations and moves. A path on a
group can encode the evolution of a dynamical system, or the moves of an
exterior observer with respect to a given system. In the theory of quantum
fields, more general objects called principal bundles, which consist in a total
space P with fibers isomorphic to a (Lie) group G over a base (simplicial
complex or manifold) .M For one of the most simple settings, one can see when
the base is a manifold (we call them continuum gauge theories) [1-5]. When the
base is a simplicial complex (or a lattice), the models are called discrete gauge
theories. They stand formally as an integrated version of the previous ones
which (more or less formally again). The physical study consists in solving
equations on P or after quantization into fields, in minimizing so-called
action functionals. These action functionals are in fact acting on connections,
which are infinitesimal expressions of local slices. They can be understood
also as differential operators. These delicate settings coming from physics
have, in the last twenty years, found two applications to our knowledge
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