# Galois Theory for Clifford Analysis and Applications to Quark Physics

Presenter: Alexandre Trovon de Carvalho, Universidade Federal do Parana, Brazil

Joint work with O. Suzuki

In this talk we introduce the idea of Galois extension for an associative algebra and show how binary and ternary algebras can be described by such an algebraic construction. Special attention is devoted to Grassmann and Clifford algebras where the binary and ternary structures emerge from Galois Extensions. Galois groups are also considered but, unlike field extensions, these will be continuous groups. Gauge invariance is also discussed in terms of Galois group of extensions. The particular ternary structure of Nonion algebra is described by means of Galois extensions, revealing the continuous $Z_3$ structure of Galois group. Ternary versions of Klein-Gordon and Dirac operators are discussed and quark models are constructed by use of Galois extensions.