We note that our gauge group is an infinite dimensional Lie group. Hence our gauge theory for soliton equations is contrasted with that of Yang-Mills equations and nonlinear Heisenberg equation in dimensions of their gauge groups [3]. First, we consider the Lagrangian action:
X = \ -fiD^dx (D = d/dx)
for scalar fields ^, T/T, i.e., wave functions on the real line R. We analyse the symmetry of X and obtain as the gauge group of the first kind a group consisting of invertible pseudo-differential operators with constant coefficients of the form:
................
Secondly, we apply the Uchiyama's gauge theory to our Lagrangian formalism.
In this case, the gauge group of the second kind...


A Unified Scheme for Generalized Sectors based on Selection ...
arxiv.org › math-ph
by I Ojima - 2002 - Related articles
20 Jun 2002 – ... we extend the Doplicher-Roberts superselection theory for recovering the field algebra and the gauge group (of the first kind) from the data of ...

Localization in algebraic field theory
www.springerlink.com/index/N305182347107896.pdf
by JE Roberts - 1982 - Cited by 11 - Related articles
of field algebras acted on by a compact gauge group of the first kind generates an additive net of observable algebras. O. Introduction. An elementary particle ...