Discrete Dynamics: Gauge Invariance and Quantization

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and internal symmetries. We describe the main features of the gauge principle relevant to the discrete and finite background. Assuming that continuous phenomena are approximations of more fundamental discrete processes, we discuss – with the help of a simple illustration – relations between such processes and their continuous approximations. We propose an approach to introduce quantum structures in discrete systems based on finite gauge groups. In this approach quantization can be interpreted as introduction of gauge connection of a special kind. We illustrate our approach to quantization by a simple model and suggest generalization of this model. One of the main tools for our study is a program written in C.

Authors and Affiliations

1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia

   Vladimir V. Kornyak

Editors and Affiliations

1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

   Vladimir P. Gerdt

2. Technische Universität München‘, Institut für Informatik, Garching, Germany

   Ernst W. Mayr

3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

   Evgenii V. Vorozhtsov

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