Generalized U(N) gauge transformations in the realm of the extended covariant Hamilton formalism of field theory

Understand

The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations.

• These gauge fields have turned out to correctly describe pertaining elementary particle interactions.
• In this paper, this principle is extended to require additionly the form-invariance of a classical field theory Hamiltonian under variations of the space-time curvature emerging from the gauge fields.
• This approach is devised on the basis of the extended canonical transformation formalism of classical field theory which allows for transformations of the space-time metric in addition to transformations of the fields.