A New Look at the Schouten-Nijenhuis, Frölicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces
نویسنده
چکیده
In this paper we re-express the Schouten-Nijenhuis, the Frölicher-Nijenhuis and the Nijenhuis-Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.
منابع مشابه
Gozzi CARTAN CALCULUS AND ITS GENERALIZATIONS VIA A PATH - INTEGRAL APPROACH TO CLASSICAL MECHANICS
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this tbrmulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets st...
متن کاملCartan Calculus and Its Generalizations via a Path-integral Approach to Classical Mechanics
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets st...
متن کاملJ an 2 00 3 Kähler - Nijenhuis Manifolds by Izu Vaisman
A Kähler-Nijenhuis manifold is a Kähler manifold M , with metric g, complex structure J and Kähler form Ω, endowed with a Nijenhuis tensor field A that is compatible with the Poisson structure defined by Ω in the sense of the theory of Poisson-Nijenhuis structures. If this happens, and if AJ = ±JA, M is foliated by im A into non degenerate Kähler-Nijenhuis submanifolds. If A is a non degenerate...
متن کاملZ-graded extensions of Poisson brackets
A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...
متن کاملThe Frölicher-Nijenhuis Calculus in Synthetic Differential Geometry
Just as the Jacobi identity of vector fields is a natural consequence of the general Jacobi identity of microcubes in synthetic differential geometry, it is to be shown in this paper that the graded Jacobi identity of the Frölicher-Nijenhuis bracket is also a natural consequence of the general Jacobi identity of microcubes.
متن کامل