A Canonical Formalism For Lagrangians With Nonlocality Of Finite Extent
نویسنده
چکیده
I consider Lagrangians which depend nonlocally in time but in such a way that there is no mixing between times differing by more than some finite value ∆t. By considering these systems as the limits of ever higher derivative theories I obtain a canonical formalism in which the coordinates are the dynamical variable from t to t+∆t. A simple formula for the conjugate momenta is derived in the same way. This formalism makes apparent the virulent instability of this entire class of nonlocal Lagrangians. As an example, the formalism is applied to a nonlocal analog of the harmonic oscillator.
منابع مشابه
Comment on “Canonical formalism for Lagrangians with nonlocality of finite extent”
In ref. [1] it is claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this short note we show that this conclusion is false.
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