Functional Lagrange formalism for time-non-local Lagrangians
Dipartimento di Fisica, Università di Trieste - Strada Costiera 11, 34151 Trieste, Italy, EU and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste - Strada Costiera 11, 34151 Trieste, Italy, EU
Accepted: 13 April 2012
We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.
PACS: 03.65.Db – Functional analytical methods / 11.10.Ef – Lagrangian and Hamiltonian approach / 02.30.Xx – Calculus of variations
© EPLA, 2012