Quantum integrability of quadratic Killing tensors
نویسندگان
چکیده
Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a “minimal” quantization scheme, quantum integrability is insured for a large class of classic examples. Preprint: CPT-2004/P.120 and LPTHE-04-33
منابع مشابه
Third rank Killing tensors in general relativity . The ( 1 + 1 ) - dimensional case
Third rank Killing tensors in (1+1)-dimensional geometries are investigated and classified. It is found that a necessary and sufficient condition for such a geometry to admit a third rank Killing tensor can always be formulated as a quadratic PDE, of order three or lower, in a Kähler type potential for the metric. This is in contrast to the case of first and second rank Killing tensors for whic...
متن کاملIntegrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano t...
متن کاملThe Variety of Integrable Killing Tensors on the 3-Sphere
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton–Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing tensors on the sphere S and give a set of isometry invariants for the integrability of a Killing tensor. We describe explicitly the space of solutions as well as i...
متن کاملNijenhuis Integrability for Killing Tensors
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...
متن کاملInvariants at Fixed and Arbitrary Energy. a Unified Geometric Approach
Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using Killing tensors we obtain an integrability condition for quadratic invariants which involves an arbitrary analytic function S(z). For invariants at arbitrary e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008