Related papers: Deformation Quantization of Superintegrable System…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
Quantization of $R^2$ and $S^1 \times S^1$ phase spaces are explicitly carried out tweaking the techniques of geometric quantization. Crucial is a combined use of left and right invariant vector fields. Canonical bases, operators and their…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for complete integrability. This severely constrains their dynamical processes, and it often leads to their exact…
The phase structure associated with the chiral symmetry is thoroughly investigated in de Sitter spacetime in the supersymmetric Nambu-Jona-Lasinio model with supersymmetry breaking terms. The argument is given in the three and four…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…
The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three…
Using Husimi function approach, we study the ``quantum phase space'' of a harmonic oscillator interacting with a plane monochromatic wave. We show that in the regime of weak chaos, the quantum system has the same symmetry as the classical…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
We extend the deformation theory algorithm of matrix factorizations to systems with more than one D-brane. The obstructions to the deformations are F-term equations which can be integrated to an effective superpotential. We demonstrate the…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
Gravitational subsystems with boundaries carry the action of an infinite-dimensional symmetry algebra, with potentially profound implications for the quantum theory of gravity. We initiate an investigation into the quantization of this…
The Hamilton-Jacobi theory is a formulation of Classical Mechanics equivalent to other formulations as Newton's equations, Lagrangian or Hamiltonian Mechanics. It is particulary useful for the identification of conserved quantities of a…
A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…