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

Rożko, Ewa Eliza; Sławianowski, Jerzy

J. Geom. Symmetry Phys. 34, 51-76 (2014).

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.

Reviewer: Werner M. Seiler (Kassel)

MSC:

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

Keywords:

Lagrangian field theories; first-order models; second-order models; gauge theory