相关论文: Hamiltonian Systems on Quantum Spaces
In this paper which is the completion of [1], we construct the $A_0(q)$-algebra of $Q$-meromorphic functions on the quantum plane. This is the largest non-commutative, associative, $A_0(q)$-algebra of functions constructed on the quantum…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…
We investigate the nonlinear holomorphic supersymmetry for quantum-mechanical systems on Riemann surfaces subjected to an external magnetic field. The realization is shown to be possible only for Riemann surfaces with constant curvature…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra,…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
In this paper we demonstrate closure of the quantum algebra of Hamiltonian constraints in a theory directly related to a certain sector of general relativity reduced to diagonal variables.