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Gauge complex field theory. (English) Zbl 1111.53022

Summary: On the total space of a computer \(G\)-vector bundle we study the gauge transformations. A gauge complex nonlinear connection determined by a gauge invariant Lagrangian plays a special role in our approach. The associated Chern-Lagrange and complex Bott connections are gauge invariant too. The complex field equations are studied with respect to a gauge invariant vertical connection, particularly with respect to the complex Bott connection.

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C05 Connections (general theory)
53C56 Other complex differential geometry
81T99 Quantum field theory; related classical field theories
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