Related papers: Symplectic Geometry on Quantum Plane

Three related topics on the quantum-vacuum geometric phases in a noncoplanarly curved optical fiber is presented: (i) a brief review: the investigation of vacuum effect and its experimental realization; (ii) the sequence of ideas of…

A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…

We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical…

In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…

We analyze the symplectic structure of two-dimensional dilaton gravity by evaluating the symplectic form on the space of classical solutions. The case when the spatial manifold is compact is studied in detail. When the matter is absent we…

In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…

In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification…

Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…

The paper deals with a cosmological model containing two scalar fields which can be considered as an extension of the Brans-Dicke scalar field model. Due to highly coupled non linear field equations, Noether Symmetry analysis has been…

We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a…

A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…

A Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory…

We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially…

We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

In this work, we explore the implications of applying the formalism of symplectic geometry to quantum mechanics, particularly focusing on many-particle systems. We extend the concept of a symplectic indicator of entanglement, originally…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This…

We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non trivial way. These systems depend on a parameter t $\in$ [0, 1] and exhibit different behaviors…

Poisson plane and sphere --- homogeneous spaces of Poisson groups E(2) and SU(2) (resp.) --- have phase spaces (corresponding symplectic groupoids), in which a free Hamiltonian is naturally defined. We solve the equations of motion and…