Elements of Field Theory with Topological Charges
Along with nonabelian gauge theories in the 1960s, the Skyrme model came to catalyze the application of homotopy theory and other machinery of algebraic topology to the study of nonlinear field theory problems. Topology and differential geometry have become a common language for particle physicists and condensed matter physicists and now geometrical concepts conquer the nuclear physics community. There exists a firm opinion that classical field theory is differential geometry endowed with physical meaning, while quantum field theory one could expect to be related to random geometry. We will not either support, nor deny this view, but rather formulate some familiar field theoretic concepts using geometrical language.
KeywordsConfiguration Space Cohomology Group Homotopy Class Topological Charge Homotopy Group
Unable to display preview. Download preview PDF.