Hamiltonian formalism for path-dependent Lagrangians

A presymplectic structure for path-dependent Lagrangian systems is set up such that, when applied to ordinary Lagrangians, it yields the familiar Legendre transformation. It is then applied to derive a Hamiltonian formalism and the conserved quantities for those predictive invariant systems whose solutions also satisfy a Fokker-type action principle

Generalized states in SFT

The search for analytic solutions in open string fields theory \ue0 la Witten often meets with singular expres- sions, which need an adequate mathematical formalism to be interpreted. In this paper we discuss this problem and propose a way to resolve the related ambiguities. Our claim is that a correct interpretation requires a formalism simi- lar to distribution theory in functional analysis. To this end we concretely construct a locally convex space of test string states together with the dual space of functionals. We show that the above suspicious expressions can be identified with well defined elements of the dual