2009/01/01 by Vladimir V. Kornyak
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #BRST quantization #Gauge fixing #Gauge theory #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Introduction to gauge theory #Lattice gauge theory #Nonlinear Waves and Solitons #Quantization (signal processing) #Supersymmetric gauge theory #math-ph #math.MP
paper · pdf · doi:10.1007/978-3-642-04103-7_17
published as Lecture Notes in Computer Science, V. 5743, pp. 180-194, Springer 2009 · 15 pages; CASC 2009, Kobe, Japan, September 13-17, 2009
openalex publication_date 2009/01/01 · arxiv created 2009/09/21 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.