Essential nonlinearity in field theory and continuum mechanics. Second- and first-order generally-covariant models. (English) Zbl 1305.81080

The authors compare the roles of first- and second-order Lagrangian models in field theories. After a short heuristic discussion of \(\mathrm U(1)\) gauge theories, the main emphasis is on the gauge group \(\mathrm{SU}(2,2)\). The authors argue that, while current physics favour first-order models like the Dirac equation, second-order models may open new perspectives.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems