1110.2968 (Daniele Venturi)

Conjugate flow action functionals    [PDF]

Daniele Venturi

We present a new method to construct an action functional for a field theory described in terms of nonlinear partial differential equations (PDEs). The key idea relies on an intrinsic representation of the PDEs governing the physical system relatively to a diffeomorphic flow of coordinates which is assumed to be a functional of their solution. This flow, which will be called the conjugate flow of the theory, evolves in space and time similarly to a physical fluid flow of classical mechanics and it can be selected in order to symmetrize the Gateaux derivative of the field equations relatively to a suitable (advective) bilinear form. This is equivalent to require that the equations of motion of the field theory can be derived from a principle of stationary action on a Lie group manifold. By using a general operator framework, we obtain the determining equations of such symmetrizing manifold for a second-order nonlinear scalar field theory. The generalization to vectorial and tensorial theories is straightforward.

View original: http://arxiv.org/abs/1110.2968