Related papers: On the Moyal quantized BKP type hierarchies
We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective…
The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined.…
The relation between the Moyal-Weyl deformation quantization and quasiconformal mappings of Riemann surfaces of complex analysis are shown by several examples.
We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic…
A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
The recently presented quantum antibrackets are generalized to quantum Sp(2)-antibrackets. For the class of commuting operators there are true quantum versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a…
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…
Using the quantum covariant Poisson bracket (QCPB) theory, we can accomplish much more compatible explanations of the quantum mechanics supported by the G-dynamics. We further study the generalized quantum harmonic oscillator equipped with…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
By using pseudo-differential operators containing two derivations, we extend the Kadomtsev-Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we obtain its B\"{a}cklund transformations, bilinear equations…
A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
It is shown that the isomorphism between the generalized Moyal algebra and the matrix algebra follows in a natural manner from the generalized Weyl quantization rule and from the well known matrix representation of the destruction and…
Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…
We derive hierarchies of separability criteria that identify the different degrees of entanglement ranging from bipartite to genuine multi-partite in mixed quantum states of arbitrary size.
We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to…
One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology…