Pure quantum integrability
نویسندگان
چکیده
منابع مشابه
Pure quantum integrability
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are polynomial in momenta one can construct a corresponding commuting set of differential operators. Here we discuss some 2or 3-dimensional purely quantum integrab...
متن کاملOn quantum integrability and Hamiltonians with pure point spectrum
We prove that any n-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set Σ ⊂ R there exists an integrable n-dimensional Hamiltonian which realizes it as its spectrum. We develop several applications of these results and discuss their implications in the general framework of quantu...
متن کاملClassical and Quantum Integrability
It is a well-known problem to decide if a classical hamiltonian system that is integrable, in the Liouville sense, can be quantised to a quantum integrable system. We identify the obstructions to do so, and show that the obstructions vanish under certain conditions. 2000 Math. Subj. Class. 81S10.
متن کاملRepresentation theory and quantum integrability ∗
We describe new constructions of the infinite-dimensional representations of U(g) and Uq(g) for g being gl(N) and sl(N). The application of these constructions to the quantum integrable theories of Toda type is discussed. With the help of these infinitedimensional representations we manage to establish direct connection between group theoretical approach to the quantum integrability and Quantum...
متن کاملOn Quantum Integrability and the Lefschetz Number
Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are a priori arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics Letters A
سال: 1998
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(98)00535-0