ar X iv : d g - ga / 9 70 30 16 v 1 2 4 M ar 1 99 7 Hamiltonian versus Lagrangian formulations of supermechanics
نویسنده
چکیده
We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects in supermechanics such as, the vertical endomorphism, the canonical and the Cartan’s graded forms, the total time derivative operator and the super–Legendre transformation. In this way, we obtain a correspondence between the Lagrangian and the Hamiltonian formulations of supermechanics.
منابع مشابه
ar X iv : d g - ga / 9 70 30 18 v 1 2 4 M ar 1 99 7 Higher order Lagrangian supermechanics
Generalized mechanics where the Lagrangian describing the system depends on higher order derivatives has been investigated in connection with relativistic dynamics of particles, supersymmetry, polymer physics, string models and gravity theory, among other problems (see, e.g., [11]). For instance, it has been proposed to add to the point particle action a term proportional to acceleration, or th...
متن کاملar X iv : c on d - m at / 9 41 20 35 v 1 7 D ec 1 99 4 IDEAL ANYONS
A general introduction to the anyon model (braid group, Chern-Simons Lagrangian and Aharonov-Bohm Hamiltonian formulations) is given. A review follows on exact results and possible ways of getting additional information, as mean field approach, perturbation theory, and projection on the lowest Landau level of an external magnetic field.
متن کاملar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES
§
متن کاملar X iv : g r - qc / 9 50 80 52 v 1 2 5 A ug 1 99 5 Evolutionary Laws , Initial Conditions , and Gauge Fixing in Constrained Systems
We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and the determination of inequivalent initial data. The Lagrangian discussion is novel, and a proof is given that the final number of degrees of freedom in the tw...
متن کاملar X iv : d g - ga / 9 50 70 04 v 1 2 4 Ju l 1 99 5 LOCALISATION OF THE DONALDSON ’ S INVARIANTS ALONG SEIBERG - WITTEN CLASSES
This article is a first step in establishing a link between the Donaldson polynomials and Seiberg-Witten invariants of a smooth 4-manifold.
متن کامل