Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-12-11
J.Phys.A34:4167-4182,2001
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, LaTeX, no figures, version to appear in J. Phys. A: Math Gen
Scientific paper
10.1088/0305-4470/34/19/314
It is shown that two$(1 + 1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (without any interaction with matter fields) belong to a new class of topological field theories. These new theories capture together some of the key features of Witten- and Schwarz type of topological field theories because they are endowed with symmetries that are reminiscent of the Schwarz type theories but their Lagrangian density has the appearance of the Witten type theories. The topological invariants for these theories are computed on a 2D compact manifold and their recursion relations are obtained. These new theories are shown to provide a class of tractable field theoretical models for the Hodge theory in two dimensions of flat (Minkowski) spacetime where there are no propagating degrees of freedom associated with the 2D gauge boson.
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